To prove that $\frac{a + b}{2} \geq ab$ for all positive real numbers $a$ and $b$ , which expression is it most useful to show is non-negative?

Practise more Proof techniques.

Free questions with an explanation for every one, and full timed TMUA mock tests.

All Proof techniques questions Take a mock test

More Proof techniques questions

A student wants to prove that the sum of two consecutive integers is always odd. Which way of writing the two integers leads to a complete p…
A proof by contradiction that there is no largest even integer begins: *'Suppose $N$ is the largest even integer.'* Which statement produces…
A student proves that the product of two odd integers is odd. Let the integers be $2 m + 1$ and $2 n + 1$ . Which expression correctly shows th…
To prove that $a^{2} + b^{2} \geq 2 ab$ for all real numbers $a$ and $b$ , which observation completes a correct proof?