Question

For what negative values of x, will ${x^{18}}$ be equal to ${x^{20}}$ ?

Answer 1

Hint: To solve this problem we need to make an equation. It’s given that ${x^{18}} = {x^{20}}$ . So we’ll equal these two variables and find the value of x when x is negative. To solve this problem, we’ll use factoring. After arranging the values we’ll find the value of x.

Complete step-by-step solution:
From the problem we need to find the negative value of x for which ${x^{18}}$ is equal to ${x^{20}}$ .So we’ll first make them equal. After that we’ll try to simplify the equation. At the end we’ll get some factors. Then we’ll make each factor equal to zero. Now we have different x values. But we need a negative value of x. So we’ll see the negative value of x and whatever will be the value that will be our answer.
So now we’ll see how we can solve it step by step.
So the equation will be
$
  {x^{18}} = {x^{20}} \\
 \Rightarrow {x^{18}} - {x^{20}} = 0 \\
\Rightarrow {x^{18}}(1 - {x^2}) = 0 \\
\Rightarrow {x^{18}}(1 - x)(1 + x) = 0 $
Therefore we can write
$ {x^{18}} = 0 $
$\Rightarrow x = 0$
Or,
$ 1 - x = 0 $
$\Rightarrow 1 = x $
$\Rightarrow x = 1$
Or,
$1+x=0 $
$\Rightarrow 1 = - x $
$\Rightarrow x = - 1 $
From these values we get x=0, x=1 and x=-1.
Now it’s given that we need to find the negative value of x.
So the negative value for which ${x^{18}}$ is equal to ${x^{20}}$ is -1.

Note: Whenever we get this kind of question always remember to equate the two values as it is said. Here they mentioned that ${x^{18}}$ will be equal to ${x^{20}}$ . So we equate these two and find the negative value of x. If it’s written as a positive value then we need to find the positive values of x. Remember what they want. Understand the question properly.