Question

If $x^2+x=30$, which of the following is a possible value of $x^2-x$?

• A. $-30$
• B. $10$
• C. $20$
• D. $30$
• E. $870$

Answer 1

The correct option is C $20$

Given

$x^2$ $+$ $x$ $=$ $30$

Solving for ${}^{\prime }{x}^{\prime }$ by factorization method, we get

$x^2$ $+$ $x$ $-$ $30$ $=$ $0$

$x^2$ $+$ $x$ $-$ $(6$ $\times$ $5)$ $=$ $0$

$x^2$ $+$ $6x$ $-$ $5x$ $-$ $(6$ $\times$ $5)$ $=$ $0$

$x(x$ $+$ $6)$ $-$ $5(x$ $+$ $6)$ $=$ $0$

$(x$ $+$ $6)$ $(x$ $-$ $5)$ $=$ $0$

Possible values of ${}^{\prime }{x}^{\prime }$ are obtained by

$(x$ $+$ $6)$ $=$ $0$ $or$ $(x$ $-$ $5)$ $=$ $0$

$x$ $=$ $-6$ $or$ $x$ $=$ $5$

To find the possible value of $x^2$ $-$ $x$,

When $x$ $=$ $-6$,

$x^2$ $-$ $x$ $=$ ${(-6)}^2$ $-$ $(-6)$

$=$ $36$ $+$ $6$

$=$ $42$

When $x$ $=$ $5$,

$x^2$ $-$ $x$ $=$ ${\left(5\right)}^2$ $-$ $\left(5\right)$

$=$ $25$ $-$ $5$

$=$ $20$

Possible values of ${}^{\prime }$$x^2$ $-$ $x$${}^{\prime }$ are ${}^{\prime }{42}^{\prime }$ and ${}^{\prime }{20}^{\prime }$.

Therefore, $\left(C\right)$ $20$ is correct.