Question:
If \(a + b + c = 0\), what is the value of \(\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\)?
यदि \(a + b + c = 0\) है, तो \(\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\) का मान क्या होगा?
Options:
- 3
- 0
- 1
- -3
- 3
- 0
- 1
- -3
Correct Answer: a)
Explanation:
Taking LCM: \(\frac{a^3 + b^3 + c^3}{abc}\).
When \(a + b + c = 0\), the standard algebraic identity gives \(a^3 + b^3 + c^3 = 3abc\).
Therefore: \(\frac{3abc}{abc} = 3\).
When \(a + b + c = 0\), the standard algebraic identity gives \(a^3 + b^3 + c^3 = 3abc\).
Therefore: \(\frac{3abc}{abc} = 3\).
ल.स. लेने पर: \(\frac{a^3 + b^3 + c^3}{abc}\)। चूंकि \(a+b+c=0\) होने पर \(a^3+b^3+c^3 = 3abc\) होता है, अतः मान 3 प्राप्त होता है।