If \sqrt{x + 4} - \sqrt{x - 1} = 1, what is the value of x? — JAMB UTME

If $\sqrt{x + 4} - \sqrt{x - 1} = 1$ , what is the value of $x$ ?

The value of

x

5

Isolating

\sqrt{x + 4}

gives

\sqrt{x + 4} = 1 + \sqrt{x - 1}

. Squaring both sides yields

x + 4 = 1 + 2\sqrt{x - 1} + x - 1

, which simplifies to

4 = 2\sqrt{x - 1}

. Dividing by 2 gives

2 = \sqrt{x - 1}

. Squaring both sides once more gives

4 = x - 1

, which leads to

x = 5

Isolate one of the surd terms on the left side of the equation.

\sqrt{x + 4} = 1 + \sqrt{x - 1}

Rearranging terms prevents dealing with complex cross-products when squaring.

Square both sides of the equation.

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

Squaring eliminates the outer radical on the left side.

Simplify both sides and isolate the remaining radical term.

4 = 2\sqrt{x - 1} \implies 2 = \sqrt{x - 1}

Subtracting

x

from both sides simplifies the algebraic expression.

Square both sides again to solve for

x

4 = x - 1 \implies x = 5

Squaring eliminates the remaining radical term.

Solving Surd Equations by Rational Elimination

Question