Question

How do you solve `(7x - 2)^(1/3) + (7x + 5)^(1/3) = 3`?

Answer 1

`x=3/7`

Explanation:

Note that if `7x=3` then:

`(7x-2)^(1/3)+(7x+5)^(1/3) = 1^(1/3) + 8^(1/3) = 1+2 = 3`

So one solution is `x=3/7`

Since `t^(1/3)` is strictly monotonically increasing, this will be the only Real solution.

graph{(y-(7x-2)^(1/3)-(7x+5)^(1/3))(y-3)=0 [-10.16, 9.84, -2.88, 7.12]}