Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation |x|=5
-
Equation x-cos(x)=0
-
Equation a+970=69*32
-
Equation t-4/25=8
- Express {x} in terms of y where:
- 19*x-19*y=6
- 5*x+2*y=-16
- -20*x+6*y=-12
- -12*x+11*y=15
- Graphing y =:
- (x^2+9)/x
- Derivative of:
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(x^2+9)/x
-
2*x
- Integral of d{x}:
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2*x
- Limit of the function:
-
2*x
-
Identical expressions
- (x^ two + nine)/x= two *x
- (x squared plus 9) divide by x equally 2 multiply by x
- (x to the power of two plus nine) divide by x equally two multiply by x
- (x2+9)/x=2*x
- x2+9/x=2*x
- (x²+9)/x=2*x
- (x to the power of 2+9)/x=2*x
- (x^2+9)/x=2x
- (x2+9)/x=2x
- x2+9/x=2x
- x^2+9/x=2x
- (x^2+9) divide by x=2*x
-
Similar expressions
- (x+3)^4+2(x+3)^2-8=0
- (x^2-9)/x=2*x
- x^2-15=2x
- 3x^2+2x-1=0
- 2^x=-4
- -6,32x=60,04
(x^2+9)/x=2*x equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$\frac{x^{2} + 9}{x} = 2 x$$
Multiply the equation sides by the denominators:
x
we get:
$$x^{2} + 9 = 2 x^{2}$$
$$x^{2} + 9 = 2 x^{2}$$
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$x^{2} + 9 = 2 x^{2}$$
to
$$9 - x^{2} = 0$$
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
$$a = -1$$
$$b = 0$$
$$c = 9$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -3$$
$$x_{2} = 3$$
$$\frac{x^{2} + 9}{x} = 2 x$$
Multiply the equation sides by the denominators:
x
we get:
$$x^{2} + 9 = 2 x^{2}$$
$$x^{2} + 9 = 2 x^{2}$$
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$x^{2} + 9 = 2 x^{2}$$
to
$$9 - x^{2} = 0$$
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
$$a = -1$$
$$b = 0$$
$$c = 9$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (-1) * (9) = 36
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -3$$
$$x_{2} = 3$$
The graph