Inequalities and equations with powers
Answers are for parents and teachers.
1
Solve x³ < −8.
x < −2
2
Solve x⁴ ≥ 1296.
x ≤ −6 or x ≥ 6
3
Solve √(x + 7) = x + 1 and check the roots.
x = 2 (x = −3 is extraneous)
4
Solve √(4x − 3) > 5.
x > 7
5
Why must the roots be checked after squaring an irrational equation? Give an example.
Squaring turns a false equality like −1 = 1 into the true 1 = 1. For example, in √(x + 6) = x the value x = −2 is extraneous.