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Other calculators
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How to use it?
- Equation:
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Equation sin(x)=sqrt2/2
- Equation √(3x^2+5x-2)=3x-1
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Equation x+125=230+25
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Equation z^3+27=0
- Express {x} in terms of y where:
- 9*x+18*y=6
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- -1*x-19*y=-10
- (x^2+y^2-1)^3+x^2*y^3=0
- Derivative of:
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3x-1
- Integral of d{x}:
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3x-1
- Graphing y =:
- 3x-1
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Identical expressions
- √(3x^ two +5x- two)=3x- one
- √(3x squared plus 5x minus 2) equally 3x minus 1
- √(3x to the power of two plus 5x minus two) equally 3x minus one
- √(3x2+5x-2)=3x-1
- √3x2+5x-2=3x-1
- √(3x²+5x-2)=3x-1
- √(3x to the power of 2+5x-2)=3x-1
- √3x^2+5x-2=3x-1
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Similar expressions
- log3(x-1)*log3((3^(x+1))+3)log(x-1)((3^x)+1)=6
- √(3x^2-5x-2)=3x-1
- √(3x^2+5x-2)=3x+1
- √(3x^2+5x+2)=3x-1
√(3x^2+5x-2)=3x-1 equation
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The solution
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________________ / 2 \/ 3*x + 5*x - 2 = 3*x - 1
$$\sqrt{\left(3 x^{2} + 5 x\right) - 2} = 3 x - 1$$
Detail solution
Given the equation
$$\sqrt{\left(3 x^{2} + 5 x\right) - 2} = 3 x - 1$$
$$\sqrt{3 x^{2} + 5 x - 2} = 3 x - 1$$
We raise the equation sides to 2-th degree
$$3 x^{2} + 5 x - 2 = \left(3 x - 1\right)^{2}$$
$$3 x^{2} + 5 x - 2 = 9 x^{2} - 6 x + 1$$
Transfer the right side of the equation left part with negative sign
$$- 6 x^{2} + 11 x - 3 = 0$$
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
$$a = -6$$
$$b = 11$$
$$c = -3$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{1}{3}$$
$$x_{2} = \frac{3}{2}$$
Because
$$\sqrt{3 x^{2} + 5 x - 2} = 3 x - 1$$
and
$$\sqrt{3 x^{2} + 5 x - 2} \geq 0$$
then
$$3 x - 1 \geq 0$$
or
$$\frac{1}{3} \leq x$$
$$x < \infty$$
The final answer:
$$x_{1} = \frac{1}{3}$$
$$x_{2} = \frac{3}{2}$$
$$\sqrt{\left(3 x^{2} + 5 x\right) - 2} = 3 x - 1$$
$$\sqrt{3 x^{2} + 5 x - 2} = 3 x - 1$$
We raise the equation sides to 2-th degree
$$3 x^{2} + 5 x - 2 = \left(3 x - 1\right)^{2}$$
$$3 x^{2} + 5 x - 2 = 9 x^{2} - 6 x + 1$$
Transfer the right side of the equation left part with negative sign
$$- 6 x^{2} + 11 x - 3 = 0$$
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
$$a = -6$$
$$b = 11$$
$$c = -3$$
, then
D = b^2 - 4 * a * c =
(11)^2 - 4 * (-6) * (-3) = 49
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{1}{3}$$
$$x_{2} = \frac{3}{2}$$
Because
$$\sqrt{3 x^{2} + 5 x - 2} = 3 x - 1$$
and
$$\sqrt{3 x^{2} + 5 x - 2} \geq 0$$
then
$$3 x - 1 \geq 0$$
or
$$\frac{1}{3} \leq x$$
$$x < \infty$$
The final answer:
$$x_{1} = \frac{1}{3}$$
$$x_{2} = \frac{3}{2}$$
Sum and product of roots
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sum
1/3 + 3/2
$$\frac{1}{3} + \frac{3}{2}$$
=
11/6
$$\frac{11}{6}$$
product
3 --- 3*2
$$\frac{3}{2 \cdot 3}$$
=
1/2
$$\frac{1}{2}$$
1/2