Question

Solve the equation using square roots.

–x2 + 16 = 0
A ; ±4
B ; ±16
C ; no real number solutions
D ; 4

Answer 1

-x² +16 = 0
x² - 16 = 0
x² = 16
x = ±√16
x = ±4

Answer: A ; ±4

Answer 2

Answer: The correct option is

(A) ±4

Step-by-step explanation: We are given to solve the following quadratic equation using the method of square roots :

`-x^2+16=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

In square root method, we should take x² term on one side and the constant the on other side of the equation Then, we should take the square roots.

From equation (i), we have

`-x^2+16=0\\\\\Rightarrow x^2=16\\\\\Rightarrow x=\pm√(16)~~~~~~~~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow x=\pm4.`

Thus, the required solution of the given equation is x = ±4.

Option (A) is CORRECT.