Solve.
-$$\sqrt { x + 60 } - \sqrt { x + 32 } = 2$$
A) $- 4$
B) 4
C) 5
D) $\varnothing$

Question

Quizplus · Accepted Answer

To solve the equation $\sqrt{x + 60} - \sqrt{x + 32} = 2$, let $y = \sqrt{x + 32}$. Then $\sqrt{x + 60} = y + 2$. Squaring both sides gives $x + 60 = (y + 2)^2$. Simplifying, we get $x + 60 = y^2 + 4y + 4$. Since $y = \sqrt{x + 32}$, we have $x + 32 = y^2$. Subtracting these equations, $x + 60 - (x + 32) = y^2 + 4y + 4 - y^2$, simplifies to $28 = 4y + 4$. Solving for $y$, we get $y = 6$. Substituting back, $\sqrt{x + 32} = 6$, so $x + 32 = 36$, giving $x = 4$.

Solve - x+60−x+32=2\sqrt { x + 60 } - \sqrt { x + 32 } = 2x+60​−x+32​=2

Solve
- $\sqrt { x + 60 } - \sqrt { x + 32 } = 2$