Q. If $a,\ b,\ c,\ d$ be in HP, then
A) $a^{2} + c^{2} > b^{2} + d^{2}$
B) $a^{2} + d^{2} > b^{2} + c^{2}$
C) $ac + bd > b^{2} + c^{2}$
D) $ac + bd > b^{2} + d^{2}$
Explanation
(c)
Since, $a,\ b,c$ be in HP.
Then, $b = \frac{2ac}{a + c}$
GM between $a$ and $c = \ \sqrt{ac}$
We know, GM > HM
$\Rightarrow \ \sqrt{ac} > b$ or $ac > b^{2}$ …(i)
Similarly, $\sqrt{bd} > c$ or $bd > c^{2}$ …(ii)
On adding relations (i) and (ii), we get
$ac + bd > b^{2} + c^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.