Answer to Question #261012 in Algebra for Master J

Question

Given that 𝑇 = 3√ 32𝑐⁴−𝑞 /2 . Show that 𝑐 = 1/2 4√2𝑇³ + 𝑞   

Answer 1

$𝑇 = \frac{\sqrt[3]{32𝑐^4−𝑞 }}{2}$

$2×T=\sqrt[3]{32𝑐^4-q}$

$2^3×T^3={32𝑐^4-q}$

$8T^3={32𝑐^4-q}$

$8T^3+q={32𝑐^4}$

$\sqrt[4]\frac{8T^3+q}{32}={𝑐}$

$c=\frac{1}{2}\sqrt[4]{2T^3+q}$