Point 6 — Radical equations

What do we see?

A radical equation with one solution or no solution.

What do we understand?

Plug selected values into Desmos — e.g. 32 and 31.75 (a number and that number minus 0.25) — and check.

Tips & traps

For f(x) = $\sqrt{x - a}$ , both x − a > 0 and the radical itself > 0. Do not simply square both sides and stop — check for extraneous roots.

Question 1 of 2

$\sqrt{k - x}$ = 32 − x

In the given equation, k is a constant. The equation has exactly one real solution. What is the minimum possible value of 4k?