Question

If
`x - 12 √(x) + 36 = 0`, what is the value of x?

A.) 6
B.) 6^2
C.) 6^3
D.) 6^4

Answer 1

x - 12√x + 36 = 0
(√x)² - 2*6√x + 6² = 0

We have a perfect square here. (a-b)² =a² - 2ab + b²,
where a= √x and b = 6,
so for our equation we can write

(√x)² - 2*6√x + 6² = (√x-6)²

(√x-6)² = 0
√x-6 = 0
√x = 6
(√x)² = 6²
x = 6²=36

Check:
x - 12√x + 36 = 0
36 - 12√36+ 36 = 0
36 -12*6 +36=0
72 - 72 = 0
0=0 True

Answer is B. 6²