√{2x +7} = x +2 | Surds - Solve | SciPiPupil

Question: Solve: $\sqrt{2x +7} = x +2$

Solution:

Given,

$\sqrt{2x +7} = x +2$

[ Squaring both sides ]

$or, (\sqrt{2x +7})^2 = (x +2)^2$

$or, 2x +7 = x^2 + 2×x×2 + 2^2$

$or, 2x +7 = x^2 +4x + 4$

$or, x^2 + 4x -2x +4 -7 = 0$

$or, x^2 +2x -3 = 0$

$or, x^2 +(3-1)x +3= 0$

$or, x^2 + 3x -x +3 = 0$

$or, x(x +3) -1(x +3) = 0$

$or, (x -1)(x +3) = 0$

Either,

$(x -1) = 0$

$\therefore x = 1$

Or,

$(x +3) = 0$

Now,

Substituting x = 1 in the given equation:

$\sqrt{2×1 + 7} = 1+2$

$or, \sqrt{2+7} = 3$

$or, \sqrt{9} = 3$

$or, 3 = 3 which is true.

Again,

Substituting x = -3 in the given equation:

$\sqrt{2×(-3) + 7} = -3 +2$

$or, \sqrt{-6+7} = -3 +2$

$or, \sqrt{1} = -1$ which is false.

Hence, x = 1.