Question

What is the solution to the equation 3\sqrt{5x-4}=3\sqrt{7x+8}?
x = –6
x = –1
x = 1
x = 2

Answer 1

Interpreting 3√ as the cube root (∛), we have ∛(5x−4)=∛(7x+8) so 5x−4=7x+8. Solve: −12=2x, x=−6. Check: cube roots are defined for all reals, so x=−6 is valid.

(If the symbol were the square root √ instead, there would be no solution because squaring gives x=−6 which doesn't satisfy the domain 5x−4 ≥ 0.)