Question
Download Solution PDFIf a, b, c are all non-zero and a + b + c = 0, find the value of \(\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}\).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
a + b + c = 0
Calculation:
⇒ \(\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}\)
⇒ Taking LCM of denominator, we get
⇒ \(\frac{a^2\times a+b^2\times b+c^2\times c}{abc}\) = \(\frac{a^3+b^3+c^3}{abc}\) → (1)
⇒ Now, a + b = –c
⇒ Cubing both the sides, we get
⇒ a3 + b3 + 3ab(a + b) = –c3
⇒ a3 + b3 + c3 = 3abc
⇒ Putting this value in (1), we get
⇒ \(\frac{a^3+b^3+c^3}{abc}\) = \(\frac{3abc}{abc}\) = 3
Therefore, the required value of \(\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}\) is 3.
Last updated on Jun 16, 2025
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