Question

PLEASE SOLVE AND CHECK. SHOW COMPLETE SOLUTION

Answer 1

Solution:

$\sqrt{4x + 13} = x + 2$

• First square both sides.

$= > ( \sqrt{4x + 13} ) ^{2} = (x + 2) ^{2}$

• Now, square root and square gets cancel out in the LHS. And in the RHS, apply the identity: (a + b)² = a² + 2ab + b².

$= > 4x + 13 = {(x)}^{2} + 2 \times x \times 2 + (2) ^{2} \\ = > 4x + 13 = {x}^{2} + 4x + 4$

• Now, transpose 4x and 4 to LHS.

$= > 4x - 4x + 13 - 4 = {x}^{2}$

• Now, do the addition and subtraction.

$= > {x}^{2} = 9 \\ = > x = \sqrt{9} \\ = > x = ±3$

Answer:

x = ± 3

Hope you could understand.

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