Question

Solve the equation $3^{x^2-x}=25-4^{x^2-x}$

• A. $-1$ only
• B. $2$ only
• C. Both $-1$ and $2$
• D. No Solution

Answer 1

Answer: (C)

Given equation $3^{x^2-x}=25-4^{x^2-x}$
$\Rightarrow 4^{x^2-x}+3^{x^2-x}=25=4^2+3^2$
$\Rightarrow x^2-x=2\Rightarrow x^2-x-2=0$
$\Rightarrow (x-2)(x+1)=0\Rightarrow x=-1,2$