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How to use it?
- Equation:
- Equation x+y=15
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Equation 4x-x^2=x^2-x+3
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Equation (x-4)/x=(2*x+10)/(x+4)
- Equation x^2+p*x+q=0
- Express {x} in terms of y where:
- -13*x+7*y=-17
- -17*x+2*y=3
- 2*x+10*y=-5
- 15*x-18*y=-10
-
Identical expressions
- two √(x- one)-√x+ two =√(5x- ten)
- 2√(x minus 1) minus √x plus 2 equally √(5x minus 10)
- two √(x minus one) minus √x plus two equally √(5x minus ten)
- 2√x-1-√x+2=√5x-10
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Similar expressions
- 2√(x-1)-√x+2=√(5x+10)
- 2√(x-1)-√x-2=√(5x-10)
- 2√(x+1)-√x+2=√(5x-10)
- 2√(x-1)+√x+2=√(5x-10)
2√(x-1)-√x+2=√(5x-10) equation
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The solution
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[src]
_______ ___ __________ 2*\/ x - 1 - \/ x + 2 = \/ 5*x - 10
$$\left(- \sqrt{x} + 2 \sqrt{x - 1}\right) + 2 = \sqrt{5 x - 10}$$
Rapid solution
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_____________________________________________________________________________________________________________________________
/ ________________
/ / ____
/ / 43 55*\/ 69 10 17
/ -2 - 2*3 / -- + --------- + ------------------------------------------------------------------ + -----------------------
________________________________________________________ / \/ 16 144 ________________________________________________________ ________________
/ ________________ / / ________________ / ____
/ / ____ / / / ____ / 43 55*\/ 69
/ / 43 55*\/ 69 17 / / / 43 55*\/ 69 17 6*3 / -- + ---------
/ -1 + 2*3 / -- + --------- - ----------------------- / / -1 + 2*3 / -- + --------- - ----------------------- \/ 16 144
/ \/ 16 144 ________________ / / \/ 16 144 ________________
/ / ____ / / / ____
/ / 43 55*\/ 69 / / / 43 55*\/ 69
/ 6*3 / -- + --------- / / 6*3 / -- + ---------
\/ \/ 16 144 \/ \/ \/ 16 144
x1 = 3 + ------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$x_{1} = \frac{\sqrt{- \frac{17}{6 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}} - 1 + 2 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}} - 2 + \frac{17}{6 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}} + \frac{10}{\sqrt{- \frac{17}{6 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}} - 1 + 2 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}}}}}{2} + 3$$
x1 = sqrt(-17/(6*(43/16 + 55*sqrt(69)/144)^(1/3)) - 1 + 2*(43/16 + 55*sqrt(69)/144)^(1/3))/2 + sqrt(-2*(43/16 + 55*sqrt(69)/144)^(1/3) - 2 + 17/(6*(43/16 + 55*sqrt(69)/144)^(1/3)) + 10/sqrt(-17/(6*(43/16 + 55*sqrt(69)/144)^(1/3)) - 1 + 2*(43/16 + 55*sqrt(69)/144)^(1/3)))/2 + 3
Sum and product of roots
[src]
sum
_____________________________________________________________________________________________________________________________
/ ________________
/ / ____
/ / 43 55*\/ 69 10 17
/ -2 - 2*3 / -- + --------- + ------------------------------------------------------------------ + -----------------------
________________________________________________________ / \/ 16 144 ________________________________________________________ ________________
/ ________________ / / ________________ / ____
/ / ____ / / / ____ / 43 55*\/ 69
/ / 43 55*\/ 69 17 / / / 43 55*\/ 69 17 6*3 / -- + ---------
/ -1 + 2*3 / -- + --------- - ----------------------- / / -1 + 2*3 / -- + --------- - ----------------------- \/ 16 144
/ \/ 16 144 ________________ / / \/ 16 144 ________________
/ / ____ / / / ____
/ / 43 55*\/ 69 / / / 43 55*\/ 69
/ 6*3 / -- + --------- / / 6*3 / -- + ---------
\/ \/ 16 144 \/ \/ \/ 16 144
3 + ------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$\frac{\sqrt{- \frac{17}{6 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}} - 1 + 2 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}} - 2 + \frac{17}{6 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}} + \frac{10}{\sqrt{- \frac{17}{6 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}} - 1 + 2 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}}}}}{2} + 3$$
=
_____________________________________________________________________________________________________________________________
/ ________________
/ / ____
/ / 43 55*\/ 69 10 17
/ -2 - 2*3 / -- + --------- + ------------------------------------------------------------------ + -----------------------
________________________________________________________ / \/ 16 144 ________________________________________________________ ________________
/ ________________ / / ________________ / ____
/ / ____ / / / ____ / 43 55*\/ 69
/ / 43 55*\/ 69 17 / / / 43 55*\/ 69 17 6*3 / -- + ---------
/ -1 + 2*3 / -- + --------- - ----------------------- / / -1 + 2*3 / -- + --------- - ----------------------- \/ 16 144
/ \/ 16 144 ________________ / / \/ 16 144 ________________
/ / ____ / / / ____
/ / 43 55*\/ 69 / / / 43 55*\/ 69
/ 6*3 / -- + --------- / / 6*3 / -- + ---------
\/ \/ 16 144 \/ \/ \/ 16 144
3 + ------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$\frac{\sqrt{- \frac{17}{6 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}} - 1 + 2 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}} - 2 + \frac{17}{6 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}} + \frac{10}{\sqrt{- \frac{17}{6 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}} - 1 + 2 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}}}}}{2} + 3$$
product
_____________________________________________________________________________________________________________________________
/ ________________
/ / ____
/ / 43 55*\/ 69 10 17
/ -2 - 2*3 / -- + --------- + ------------------------------------------------------------------ + -----------------------
________________________________________________________ / \/ 16 144 ________________________________________________________ ________________
/ ________________ / / ________________ / ____
/ / ____ / / / ____ / 43 55*\/ 69
/ / 43 55*\/ 69 17 / / / 43 55*\/ 69 17 6*3 / -- + ---------
/ -1 + 2*3 / -- + --------- - ----------------------- / / -1 + 2*3 / -- + --------- - ----------------------- \/ 16 144
/ \/ 16 144 ________________ / / \/ 16 144 ________________
/ / ____ / / / ____
/ / 43 55*\/ 69 / / / 43 55*\/ 69
/ 6*3 / -- + --------- / / 6*3 / -- + ---------
\/ \/ 16 144 \/ \/ \/ 16 144
3 + ------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$\frac{\sqrt{- \frac{17}{6 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}} - 1 + 2 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}} - 2 + \frac{17}{6 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}} + \frac{10}{\sqrt{- \frac{17}{6 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}} - 1 + 2 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}}}}}{2} + 3$$
=
_____________________________________________________________________________________________________________________________
/ ________________
/ / ____
/ / 43 55*\/ 69 10 17
/ -2 - 2*3 / -- + --------- + ------------------------------------------------------------------ + -----------------------
________________________________________________________ / \/ 16 144 ________________________________________________________ ________________
/ ________________ / / ________________ / ____
/ / ____ / / / ____ / 43 55*\/ 69
/ / 43 55*\/ 69 17 / / / 43 55*\/ 69 17 6*3 / -- + ---------
/ -1 + 2*3 / -- + --------- - ----------------------- / / -1 + 2*3 / -- + --------- - ----------------------- \/ 16 144
/ \/ 16 144 ________________ / / \/ 16 144 ________________
/ / ____ / / / ____
/ / 43 55*\/ 69 / / / 43 55*\/ 69
/ 6*3 / -- + --------- / / 6*3 / -- + ---------
\/ \/ 16 144 \/ \/ \/ 16 144
3 + ------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------
2 2
$$\frac{\sqrt{- \frac{17}{6 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}} - 1 + 2 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}} - 2 + \frac{17}{6 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}} + \frac{10}{\sqrt{- \frac{17}{6 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}} - 1 + 2 \sqrt[3]{\frac{43}{16} + \frac{55 \sqrt{69}}{144}}}}}}{2} + 3$$
3 + sqrt(-1 + 2*(43/16 + 55*sqrt(69)/144)^(1/3) - 17/(6*(43/16 + 55*sqrt(69)/144)^(1/3)))/2 + sqrt(-2 - 2*(43/16 + 55*sqrt(69)/144)^(1/3) + 10/sqrt(-1 + 2*(43/16 + 55*sqrt(69)/144)^(1/3) - 17/(6*(43/16 + 55*sqrt(69)/144)^(1/3))) + 17/(6*(43/16 + 55*sqrt(69)/144)^(1/3)))/2