Question

Solve (t+2)^3/4 =2 where t is a real number.t=

Answer 1

To solve

$(t+2)^{\frac{3}{4}}=2$

for t, first, we raise the equation to the power of four:

$(t+2)^3=2^4\text{.}$

Simplifying we get:

$(t+2)^3=16.$

Therefore:

$t+2=\sqrt[3]{16}.$

Finally, we get:

$t=\sqrt[3]{16}-2=\sqrt[3]{8\cdot2}-2=2\sqrt[3]{2}-2=2(\sqrt[3]{2}-1)\text{.}$

Answer:

$t=2(2^{\frac{1}{3}}-1)\text{.}$