JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(p\) and \(q\) be two real numbers such that \(p+q=\) 3 and \(p^{4}+q^{4}=369\). Then \(\left(\frac{1}{p}+\frac{1}{q}\right)^{-2}\) is equal to
- A \(2\)
- B \(1\)
- C \(4\)
- D \(5\)
Answer & Solution
Correct Answer
(C) \(4\)
Step-by-step Solution
Detailed explanation
\(p + q =3 \quad p ^{4}+ q ^{4}=369\) \(\left(\frac{1}{p}+\frac{1}{q}\right)^{-2}\) \((p+q)^{2}=9\) \(p ^{2}+ q ^{2}=9-2 pq\) \(\frac{1}{\left(\frac{1}{p}+\frac{1}{q}\right)^{2}}=\frac{(q p)^{2}}{(q+p)^{2}}=\frac{(q p)^{2}}{9}\)…
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