Question

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

Answer 1

Solution:

Given the equation:

$\begin{gathered} (t+2)^{\frac{3}{4}}=2 \\ \text{where t is a real number} \end{gathered}$

step 1: Take both sides of the equation to the power of 4.

Thus,

$\begin{gathered} ((t+2)^{\frac{3}{4}})^4=(2)^4 \\ \Rightarrow(t+2)^3=16 \end{gathered}$

step 2: Take the cube root of both sides of the equation.

Thus,

$\begin{gathered} \sqrt[3]{(t+2)^3}=\sqrt[3]{16} \\ \Rightarrow(t+2)=16^{\frac{1}{3}} \\ \end{gathered}$

step 3: Solve for t.

$\begin{gathered} 16^{\frac{1}{3}}^{} \\ \text{can be rewritten as} \\ (2^4)^{\frac{1}{3}}=2^{\frac{4}{3}} \\ \text{thus, we have} \\ t+2=2^{\frac{4}{3}} \\ \text{subtract 2 from both sides of the equation} \\ t+2-2=2^{\frac{4}{3}}-2 \\ \Rightarrow t=2(2^{\frac{1}{3}}-1) \\ =2(1.25992-1) \\ \Rightarrow t=2(0.25992) \\ \therefore t=0.51984 \end{gathered}$

Hence, the value of t in the equation is evaluated to be 0.51984.