If √ (2x + 2) − √x =1 ,find x.

Mathematics

JAMB 2015

A. x = 1 twice
B. x = 0 or 1
C. x = 3 or 1
D. x = 2 twice

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Correct Answer: Option A

Explanation

√(2x + 2 ) − √x = 1

√(2x + 2) = 1 + √x

Square both sides

√(2x + 2)² = (1 + √x)²

((2x + 2)²)^½ = 1 + √x + √x+ x

2x + 2 = 1 + 2√x +x

Collect the like term together

2x − x + 2 − 1 = 2 √x
x + 1 = 2√x

Square both sides

(x + 1)² = (2√x)²

x² + 2x + 1 = 4x

x² + 2x − 4x + 1 = 0

(x²− x)(x + 1)= 0

x(x − 1) −1(x − 1)

(x − 1)(x −1)

Either (x − 1) = 0 or (x − 1) = 0

x = 1 or 1

x = 1 twice

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