Question

hat is the value of z?



3
√
z
−
8
=
√
z

4


9


16


25

Answer 1

Let t = √z (so t ≥ 0). Then z = t^2 and the equation becomes
3√(t^2 − 8) = t.
Square both sides: 9(t^2 − 8) = t^2 → 8t^2 = 72 → t^2 = 9 → t = 3 (reject −3 since t ≥ 0).
Thus z = t^2 = 9.