Question

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

Answer 1

To solve

`(t+2)^{(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^{(1)/(3)}-1)\text{.}`