Question

If $a,b,c,d$ are positive numbers, then $ab+cd<2\sqrt{abcd}$

• A. True
• B. False

Answer 1

The correct option is B

False

As $a,b,c,d$ are positive numbers, So $ab,cd$ are also positive

Now as AM > GM

$\frac{ab+cd}{2}>\sqrt[2]{2\left(ab\right)\left(cd\right)}$

$\Rightarrow ab+cd>2$ $\sqrt{abcd}$

Hence given statement is False.