a) Find the solution set for each of the following equations in \( \mathbb{R} \):
1. \( x^3 - 11 = 5 \)
∵ \( x^3 - 11 = 5 \)
∴ \( x^3 = 5 + 11 = 16 \) ∴ \( x = \sqrt[3]{16} \)
∴ The solution set = \( \left\{ \sqrt[3]{16} \right\} \)
2. \( 2x^3 + 13 = 67 \)
∵ \( 2x^3 + 13 = 67 \)
∴ \( 2x^3 = 67 - 13 = 54 \)
∴ \( x^3 = 54 ÷ 2 = 27 \) ∴ \( x = \sqrt[3]{27} = 3 \)
∴ The solution set = \( \left\{ 3 \right\} \)
MR/Nasef.N
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