Question

What is the solution of
$\sqrt{x + 12} = x$
a. x=-3
b. x=4
c. x=-3 or x=4
d. no solution ​

Answer 1

Answer:

Given :-

$\sqrt{x + 2 } = x$

To Find :-

The solution of X

Solution :-

$\sqrt{x + 2 } = x$

Now, squaring on both sides ,

⟹ $(\sqrt{x + 2 })² = (x)²$

⟹ x + 12 = x²

⟹ x² - x - 12 = 0

Now , doing middle term factorisation ,

⟹ x² - ( 4 - 3) x - 12 = 0

⟹ x² - 4x + 3x - 12 = 0

⟹ x ( x - 4) + 3 ( x - 4 ) = 0

⟹ ( x - 4 ) ( x + 3) = 0

Therefore,

The above solution has two values of x

⟹ ( x - 4 ) = 0

⟹ x = 4

⟹ ( x + 3 ) = 0

⟹ x = -3

The values of x are 4 and -3 respectively.