Let a , b be two non-zero real numbers. If p and r are roots of equation x ^{2}-8 ax +2 a =0 and q a

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8. Sequences and Series

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Let $a$, $b$ be two non-zero real numbers. If $p$ and $r$ are the roots of the equation $x ^{2}-8 ax +2 a =0$ and $q$ and $s$ are the roots of the equation $x^{2}+12 b x+6 b$ $=0$, such that $\frac{1}{ p }, \frac{1}{ q }, \frac{1}{ r }, \frac{1}{ s }$ are in A.P., then $a ^{-1}- b ^{-1}$ is equal to $......$

$37$

$36$

$38$

$32$

(JEE MAIN-2022)

$x ^{2}-8 ax +2 a =0$

$p + r =8 a$

$pr =2 a$

$\frac{1}{ p }+\frac{1}{ r }=4$

$\frac{2}{ q }=4$

$q =\frac{1}{2}$

$p =\frac{1}{5}$

$x^{2}+12 b x+6 b=0$

$q+s=-12 b$

$q s=6 b$

$\frac{1}{q}+\frac{1}{s}=-2$

$\frac{2}{r}=-2$

$r=-1$

$s=\frac{-1}{4}$

Now,$\frac{1}{ a }-\frac{1}{ b }=\frac{2}{ pr }-\frac{6}{ qs }=38$

Standard 11

Mathematics

hard

normal

hard

(JEE MAIN-2024)

easy

easy