If \frac{\sqrt{x} + \sqrt{3}}{\sqrt{x} - \sqrt{3}} = 2, find the value of x. — JAMB UTME

If $\frac{\sqrt{x} + \sqrt{3}}{\sqrt{x} - \sqrt{3}} = 2$ , find the value of $x$ .

Answer: 27

The value of

x

is 27.

Cross-multiplying yields

\sqrt{x} + \sqrt{3} = 2\sqrt{x} - 2\sqrt{3}

. Rearranging terms gives

\sqrt{x} = 3\sqrt{3}

. Squaring both sides produces

x = 3^2 \times 3 = 27

Multiply both sides by the denominator

(\sqrt{x} - \sqrt{3})

\sqrt{x} + \sqrt{3} = 2(\sqrt{x} - \sqrt{3})

Clear the rational surd expression to form a linear relation in terms of radicals

Expand the terms and isolate

\sqrt{x}

\sqrt{x} = 3\sqrt{3}

Group terms involving

\sqrt{x}

on one side and constant surds on the other side

Square both sides of the simplified equation

x = (3\sqrt{3})^2 = 9 \times 3 = 27

Eliminate the radical over

x

to obtain the integer solution

Solving algebraic surd equations using rationalization concepts and properties of radicals

Estimated Time:1m 30s

Question