Question

I need an accurate answer please

Answer 1

x = –6

Solution:

Given expression is $\sqrt[3]{x-2}+5=3$.

Step 1: Isolate the radical by subtracting 5 from both sides of the equation.

$\Rightarrow\sqrt[3]{x-2}+5-5=3-5$

$\Rightarrow\sqrt[3]{x-2}=-2$

Step 2: Cube both sides of the equation to remove the cube root.

$\Rightarrow(\sqrt[3]{x-2})^3=(-2)^3$

Cube and cube root get canceled in left side of the equation.

$\Rightarrow\ x-2=-8$

Step 3: To solve for x.

Add 2 on both sides of the equation.

$\Rightarrow\ x-2+2=-8+2$

$\Rightarrow\ x=-6$

Hence the solution is x = –6.