An Equation to satisfy

Algebra Level 1

What real value of x x satisfies the equation

x 3 2 x 2 x 2 = 5 ? \frac{x^3-2x^2}{x^2}=5?


The answer is 7.

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12 solutions

Chin Fong Wong
Sep 2, 2013

x 3 2 x 2 x 2 = 5 \frac{x^3 - 2x^2}{x^2}=5 , x is not equal to 0

x 3 2 x 2 = 5 x 2 x^3 - 2x^2 = 5x^2

x 3 7 x 2 = 0 x^3 - 7x^2 = 0

x 2 ( x 7 ) x^2(x - 7)

x = 0 , 7 x=0 , 7

reject 0 and hence, x = 7 x=7

Moderator note:

A mistake that is often made, is to forget that 0 0 cannot be a solution, because we end up dividing by 0.

This mistake was also made in a much harder question in this weeks set.

oh my god i can't understand everything.

Jhay L Natividad - 7 years, 9 months ago

0 it is a possible solution.

Manuel Ignacio López Quintero - 7 years, 9 months ago

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no 0 is not a possible solution because 0/0 is not possible.

lalan patel - 7 years, 9 months ago

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For x^3-2x^2 = 5x^2, 0 it is a possible solution.

Manuel Ignacio López Quintero - 7 years, 9 months ago

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@Manuel Ignacio López Quintero Indeed, 0 is a possible solution for x^3-2x^2 = 5x^2, but not our question up there. If you substitute x=0 into the equation there, your answer is undefined, since no number can be divided by 0.

Chin Fong Wong - 7 years, 9 months ago

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@Chin Fong Wong Ok, I understand it. Thanks.

Manuel Ignacio López Quintero - 7 years, 9 months ago
Lava Lamp
Sep 2, 2013

( x 3 2 x 2 ) / x 2 (x^3 - 2x^2)/x^2 simplifies to x 2 x - 2 , so we have the equation x 2 = 5 x - 2 = 5 . By adding 2 to both sides of the equation, we end up with x = 7 x = 7 .

x 3 2 x 2 x 2 = 5 \frac {x^3 - 2x^2}{x^2} = 5

x 2 ( x 2 ) x 2 = 5 \frac {x^2(x - 2)}{x^2} = 5

divide the nominator's x^2 with the denominator's x^2, so it becomes

x 2 = 5 x - 2 = 5

x = 5 + 2 x = 5 + 2

x = 7 x = 7

Moderator note:

As pointed out, you cannot simply "divide by x 2 x^2 ", unless you have verified that it is non-zero.

arigato gozamusi

Vineet Advani - 7 years, 9 months ago

it is not actually possible to divide the numerator with x^2, unless there was an assumption that x is not equal to zero.

Francis Parcasio - 7 years, 9 months ago
Eduardo Teruo
Sep 1, 2013

x³-2x²/x² = 5 => x-2=5 => x=5+2 => x=7

Get the common of the expression on the left side then cancel out x2. Then transpose 2 to the right side,add up to 5, it will become 7..That's it!!!

Rishabh Anand
Sep 5, 2013

First you should cross multiply to get x^3 - 2x^2 = 5x^2. Bring the 5x^2 to the other side through subtraction to get x^3 - 7x^2 = 0. Take x^2 out of both terms to get x^2(x - 7) = 0. x can equal either 0 or 7.

Cross multiplying, we get x^3-2x^2=5x^2. Therefore x^3=7x^2. Therefore x^1=7. Or x=7

Moderator note:

Be careful with cross-multiplying. You might introduce an addition solution, like 0 in this case. This solution is incomplete.

Henrique Mf
Sep 4, 2013

( \frac{x^3- 2x^2}{x^2} ) = 5 x-2=5 x=5+2=7

make it poly nomial form and solve we get three solutio 0,0,7 so 7 is real solution

Why isn't 0 a solution then? Is 0 not real?

Calvin Lin Staff - 7 years, 9 months ago
Farooq Mukhtar
Sep 3, 2013

equation whichcan written as x^3/x^2 - 2x^2/x^2=5, ,x^1-2 =5, x=5+2, =7

Given eqn is x3−2x2x2=5 x3 = 7x2 so,x=7 satisfies the given equation

Abhishek Misra
Sep 2, 2013

x^3-2x^2=5x^2; x^3-2x^2-5x^2=0 x^2(x-7)=0 either x=0 or x=7 but x can't be equal to 0 for real value of x hence x=7

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