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Sequences and Series question

2022 · 25 Jul · Shift 1 · Q39
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  5. /2022 · 25 Jul · Shift 1 · Q39

Sequences and Series question

2022 · 25 Jul · Shift 1 · Q39

JEE MainMathematicsSequences and SeriesNumerical+4 / −1
Let a,ba, ba,b be two non-zero real numbers. If ppp and rrr are the roots of the equation x2−8ax+2a=0x^{2}-8 \mathrm{a} x+2 \mathrm{a}=0x2−8ax+2a=0 and q\mathrm{q}q and s are the roots of the equation x2+12 bx+6 b=0x^{2}+12 \mathrm{~b} x+6 \mathrm{~b}=0x2+12 bx+6 b=0, such that 1p,1q,1r,1 s\frac{1}{\mathrm{p}}, \frac{1}{\mathrm{q}}, \frac{1}{\mathrm{r}}, \frac{1}{\mathrm{~s}}p1​,q1​,r1​, s1​ are in A.P., then a−1−b−1\mathrm{a}^{-1}-\mathrm{b}^{-1}a−1−b−1 is equal to ‾\underline{\hspace{2cm}}​.
Numerical answer
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