QJEEM21Ma1ab3: JEE Main 2021 Mathematics - Class 11 JEEM21Ma1ab3 Solution: Let , a and b be in G.P. and , , 6 be in A.P., where a, b > 0.…

Question

Verified Solution • 2025–26 Session moderate

Let

{1 \over {16}}

, a and b be in G.P. and

{1 \over a}

,

{1 \over b}

, 6 be in A.P., where a, b > 0. Then 72(a + b) is equal to ___________.

Accepted Answer

{a^2} = {b \over {16}}

and

{2 \over b} = {1 \over a} + 6

Solving, we get

a = {1 \over {12}}

or

a = - {1 \over 4}

[rejected]

if

a = {1 \over {12}} \Rightarrow b = {1 \over 9}

\therefore

72(a + b) = 72\left( {{1 \over {12}} + {1 \over 9}} \right) = 14

Step-by-Step Verified Solution