Review question

# Can we solve this equation with a sum of square roots? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6653

## Question

1. Sketch the curve $y = \sqrt{1 - x} + \sqrt{3 + x}$. Use your sketch to show that only one real value of $x$ satisfies $\sqrt{1 - x} + \sqrt{3 + x} = x + 1,$ and give this value.

2. Determine graphically the number of real values of $x$ that satisfy $2\sqrt{1 - x} = \sqrt{3 + x} + \sqrt{3 - x}.$ Solve this equation.