Question

5. If x and y are positive real numbers and m, n are any positive integers, then *(1 +32")(1+30 (1989, 1M) n are n positive intparna 6 n. n

JEE/Engineering Exams

Maths

Solution

137

4.0 (1 ratings)

5. Using AM ( geq ) GM. [ frac{1+x^{2 n}}{2} geq sqrt{1 cdot x^{2 n}} ] ( Rightarrow quad frac{1+x^{2 n}}{2} geq x^{n} ) ( Rightarrow quad frac{x^{n}}{1+x^{2 n}} leq frac{1}{2} ) ( therefore quad frac{x^{n} cdot y^{m}}{left(1+x^{2 n}right)left(1+y^{2 m}right)} leq frac{1}{4} ) Hence, it is a false statement.