Question
Download Solution PDFयदि p = \(\frac{\sqrt{2}+1}{\sqrt{2}-1}\) और q = \(\frac{\sqrt{2}-1}{\sqrt{2}+ 1}\) है, तो \(\frac{p^2}{q}+\frac{q^2}{p}\) का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया:
p = \(\frac{√{2}+1}{√{2}-1}\) और q = \(\frac{√{2}-1}{√{2}+1}\)
प्रयुक्त अवधारणा:
पी = 1 / क्यू
गणना:
पी = \(\frac{√{2}+1}{√{2}-1}\)
= ( √2 + 1) 2
⇒ 3 + 2√2
दोबारा,
क्यू = \(\frac{√{2}-1}{√{2}+1}\)
= 3 - 2 √2
पी + क्यू = 3 + 2√2 + 3 - 2√2 = 6
पीक्यू = (3 + 2√2)(3 - 2√2) = 1
हम जानते हैं कि,
p3 + q3 = (p + q)3 - 3pq(p + q)
⇒ p3 + q3 = (6)3 - 3 × 1 × 6 = 216 - 3 × 6 = 216 - 18 = 198
अब, p2/q + q2/p = (p3 + q3)/pq = 198/1 = 198
∴ सही विकल्प 3 है
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