Question
Download Solution PDFयदि a, b, c सभी शून्येतर हैं और a + b + c = 0 है, तो \(\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}\) का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
a + b + c = 0
गणना:
⇒ \(\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}\)
⇒ हर का LCM लेने पर, हमें मिलता है
⇒ \(\frac{a^2\times a+b^2\times b+c^2\times c}{abc}\) = \(\frac{a^3+b^3+c^3}{abc}\) → (1)
⇒ अब, a + b = –c
⇒ दोनों पक्षों को घन करने पर, हम प्राप्त करते हैं
⇒ a3 + b3 + 3ab(a + b) = –c3
⇒ a3 + b3 + c3 = 3abc
⇒ इस मान को (1) में रखने पर, हमें प्राप्त होता है
⇒ \(\frac{a^3+b^3+c^3}{abc}\) = \(\frac{3abc}{abc}\) = 3
इसलिए, \(\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}\) का आवश्यक मान 3 है।
Last updated on Jun 17, 2025
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