Mister Exam
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How to use it?
- Express {x} in terms of y where:
- 60x^2y+75x^2y^2+120xy^260x2y+75x2y2+120xy2приx=-0,5x=−0,5,y=0,4y=0,4.
- (x-17)^2+(y+26)^2=16(x−17)2+(y+26)2=16.
- 5*x-5*y=20
- 8*x-7*y=-13
- Equation:
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Equation 14-4x^2-x=0
- Equation 7x^2+6x-9=-x^2+14-3
- Equation z^4=i
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Equation 836-16*m=420
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Identical expressions
- 6 zero x^ two y+7 five x^2y^2+12 zero xy^26 zero x2y+75x2y2+12 zero xy2приx=-0,5x=−0,5,y=0, four y=0,4.
- 60x squared y plus 75x squared y squared plus 120xy squared 60x2y plus 75x2y2 plus 120xy2приx equally minus 0,5x equally −0,5,y equally 0,4y equally 0,4.
- 6 zero x to the power of two y plus 7 five x squared y squared plus 12 zero xy squared 6 zero x2y plus 75x2y2 plus 12 zero xy2приx equally minus 0,5x equally −0,5,y equally 0, four y equally 0,4.
- 60x2y+75x2y2+120xy260x2y+75x2y2+120xy2приx=-0,5x=−0,5,y=0,4y=0,4.
- 60x²y+75x²y²+120xy²60x2y+75x2y2+120xy2приx=-0,5x=−0,5,y=0,4y=0,4.
- 60x to the power of 2y+75x to the power of 2y to the power of 2+120xy to the power of 260x2y+75x2y2+120xy2приx=-0,5x=−0,5,y=0,4y=0,4.
- 60x^2y+75x^2y^2+120xy^260x2y+75x2y2+120xy2приx=-0,5x=−0,5,y=O,4y=O,4.
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Similar expressions
- 60x^2y+75x^2y^2+120xy^260x2y+75x2y2+120xy2приx=+0,5x=−0,5,y=0,4y=0,4.
- 60x^2y-75x^2y^2+120xy^260x2y+75x2y2+120xy2приx=-0,5x=−0,5,y=0,4y=0,4.
- 60x^2y+75x^2y^2-120xy^260x2y+75x2y2+120xy2приx=-0,5x=−0,5,y=0,4y=0,4.
- 60x^2y+75x^2y^2+120xy^260x2y+75x2y2-120xy2приx=-0,5x=−0,5,y=0,4y=0,4.
- 60x^2y+75x^2y^2+120xy^260x2y-75x2y2+120xy2приx=-0,5x=−0,5,y=0,4y=0,4.
Express x in terms of y where 60x^2y+75x^2y^2+120xy^260x2y+75x2y2+120xy2приx=-0,5x=−0,5,y=0,4y=0,4.
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The solution
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2 2 2 260 2 -x
60*x *y + 75*x *y + 120*x*y *x2*y + 75*x2*y2 + 120*x*y *pi*pi*x = ---
2
$$x \pi \pi 120 x y^{2} + \left(75 x_{2} y_{2} + \left(y x_{2} \cdot 120 x y^{260} + \left(60 x^{2} y + 75 x^{2} y^{2}\right)\right)\right) = - \frac{x}{2}$$
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$x \pi \pi 120 x y^{2} + \left(75 x_{2} y_{2} + \left(y x_{2} \cdot 120 x y^{260} + \left(60 x^{2} y + 75 x^{2} y^{2}\right)\right)\right) = - \frac{x}{2}$$
to
$$\frac{x}{2} + \left(x \pi \pi 120 x y^{2} + \left(75 x_{2} y_{2} + \left(y x_{2} \cdot 120 x y^{260} + \left(60 x^{2} y + 75 x^{2} y^{2}\right)\right)\right)\right) = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 75 y^{2} + 120 \pi^{2} y^{2} + 60 y$$
$$b = 120 x_{2} y^{261} + \frac{1}{2}$$
$$c = 75 x_{2} y_{2}$$
, then
The equation has two roots.
or
$$x_{1} = \frac{- 120 x_{2} y^{261} + \sqrt{- 75 x_{2} y_{2} \left(300 y^{2} + 480 \pi^{2} y^{2} + 240 y\right) + \left(120 x_{2} y^{261} + \frac{1}{2}\right)^{2}} - \frac{1}{2}}{150 y^{2} + 240 \pi^{2} y^{2} + 120 y}$$
$$x_{2} = \frac{- 120 x_{2} y^{261} - \sqrt{- 75 x_{2} y_{2} \left(300 y^{2} + 480 \pi^{2} y^{2} + 240 y\right) + \left(120 x_{2} y^{261} + \frac{1}{2}\right)^{2}} - \frac{1}{2}}{150 y^{2} + 240 \pi^{2} y^{2} + 120 y}$$
left part with negative sign.
The equation is transformed from
$$x \pi \pi 120 x y^{2} + \left(75 x_{2} y_{2} + \left(y x_{2} \cdot 120 x y^{260} + \left(60 x^{2} y + 75 x^{2} y^{2}\right)\right)\right) = - \frac{x}{2}$$
to
$$\frac{x}{2} + \left(x \pi \pi 120 x y^{2} + \left(75 x_{2} y_{2} + \left(y x_{2} \cdot 120 x y^{260} + \left(60 x^{2} y + 75 x^{2} y^{2}\right)\right)\right)\right) = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 75 y^{2} + 120 \pi^{2} y^{2} + 60 y$$
$$b = 120 x_{2} y^{261} + \frac{1}{2}$$
$$c = 75 x_{2} y_{2}$$
, then
D = b^2 - 4 * a * c =
(1/2 + 120*x2*y^261)^2 - 4 * (60*y + 75*y^2 + 120*pi^2*y^2) * (75*x2*y2) = (1/2 + 120*x2*y^261)^2 - 75*x2*y2*(240*y + 300*y^2 + 480*pi^2*y^2)
The equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{- 120 x_{2} y^{261} + \sqrt{- 75 x_{2} y_{2} \left(300 y^{2} + 480 \pi^{2} y^{2} + 240 y\right) + \left(120 x_{2} y^{261} + \frac{1}{2}\right)^{2}} - \frac{1}{2}}{150 y^{2} + 240 \pi^{2} y^{2} + 120 y}$$
$$x_{2} = \frac{- 120 x_{2} y^{261} - \sqrt{- 75 x_{2} y_{2} \left(300 y^{2} + 480 \pi^{2} y^{2} + 240 y\right) + \left(120 x_{2} y^{261} + \frac{1}{2}\right)^{2}} - \frac{1}{2}}{150 y^{2} + 240 \pi^{2} y^{2} + 120 y}$$