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Q. Let . Show that
- Apply AM-GM Inequality: We'll start by applying the AM-GM inequality, which states that for non-negative numbers, the arithmetic mean is greater than or equal to the geometric mean.So, .
- Simplify Right Side: Now, let's simplify the right side of the inequality..
- Raise to Power of : Raise both sides of the inequality to the power of to get rid of the cube root. .
- Multiply by : Multiplying both sides of the inequality by (which is ) gives us:
- Expand Using Binomial Theorem: Now, we'll expand the left side of the inequality using the binomial theorem. .Oops, this is incorrect. We should have expanded , not just the squared terms.
