Find all real solutions of the equation $x ^ { 4 } = 16 x ^ { 2 }$
A) $x = 0$
B) $x = 0 , x = 4 , x = - 4$
C) $x = 0 , x = 16$
D) $x = 0 , x = 16 , x = - 16$
E) none of these

Question

Find all real solutions of the equation $x ^ { 4 } = 16 x ^ { 2 }$ 
A) $x = 0$
B) $x = 0 , x = 4 , x = - 4$
C) $x = 0 , x = 16$
D) $x = 0 , x = 16 , x = - 16$
E) none of these

Quizplus · Accepted Answer

We can rewrite the equation as $x ^ { 2 } (x ^ { 2 } - 16) = 0$. Then we have two cases: either $x ^ { 2 } = 0$, which gives $x = 0$ as a solution, or $x ^ { 2 } - 16 = 0$, which gives $x = 4$ or $x = -4$ as solutions. Therefore, the solutions are $x = 0 , x = 4$ and $x = -4$, which is given in Choice B.

Find All Real Solutions of the Equation x4=16x2x ^ { 4 } = 16 x ^ { 2 }x4=16x2

Find All Real Solutions of the Equation $x ^ { 4 } = 16 x ^ { 2 }$