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JAMB Mathematics 2015 Paper

Question : 53

Total: 61

If √ (2x + 2) − √x =1 ,find x.

Solution:

Concept:

Isolate one radical, then square both sides and solve the resulting equation.

Explanation:

Start with

\sqrt{2x+2} - \sqrt{x} = 1

Isolate the radical:

\sqrt{2x+2} = 1 + \sqrt{x}

Square both sides:

2x + 2 = 1 + 2\sqrt{x} + x

Simplify:

x + 1 = 2\sqrt{x}

Square both sides again:

(x + 1)^2 = (2\sqrt{x})^2

This gives

x^2 + 2x + 1 = 4x

Rearrange:

x^2 - 2x + 1 = 0

Factor:

(x - 1)^2 = 0

Therefore,

x - 1 = 0

twice, so

x = 1

twice.

Check:

\sqrt{2(1)+2} - \sqrt{1} = \sqrt{4} - 1 = 2 - 1 = 1

The solution is valid.

Answer:

x = 1

twice, which is option A.

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