Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x+6)^3=25*(x+6)
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Equation 1-5x=-6x+8
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Equation 1-5*x=-6*x+8
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Equation (x-2)^2=(x-9)^2
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- Graphing y =:
- x+2/x
- Limit of the function:
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x+2/x
- Integral of d{x}:
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x+2/x
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Identical expressions
- x+ two /x= three
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- (x^2+x+2)/(x^2-2x+а^2+6а)=0
x+2/x=3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$x + \frac{2}{x} = 3$$
Multiply the equation sides by the denominators:
and x
we get:
$$x \left(x + \frac{2}{x}\right) = 3 x$$
$$x^{2} + 2 = 3 x$$
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$x^{2} + 2 = 3 x$$
to
$$x^{2} - 3 x + 2 = 0$$
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
$$a = 1$$
$$b = -3$$
$$c = 2$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = 1$$
$$x + \frac{2}{x} = 3$$
Multiply the equation sides by the denominators:
and x
we get:
$$x \left(x + \frac{2}{x}\right) = 3 x$$
$$x^{2} + 2 = 3 x$$
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$x^{2} + 2 = 3 x$$
to
$$x^{2} - 3 x + 2 = 0$$
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
$$a = 1$$
$$b = -3$$
$$c = 2$$
, then
D = b^2 - 4 * a * c =
(-3)^2 - 4 * (1) * (2) = 1
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = 1$$
The graph