Question:
If \(a + b + c = 18\) and \(ab + bc + ca = 92\), find the value of \(a^2 + b^2 + c^2\).
यदि \(a + b + c = 18\) और \(ab + bc + ca = 92\) है, तो \(a^2 + b^2 + c^2\) का मान ज्ञात कीजिए।
Options:
- 140
- 152
- 160
- 164
- 140
- 152
- 160
- 164
Correct Answer: a)
Explanation:
Using the algebraic identity: \((a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)\).
\(18^2 = a^2 + b^2 + c^2 + 2(92) \implies 324 = a^2 + b^2 + c^2 + 184 \implies a^2 + b^2 + c^2 = 324 – 184 = 140\).
सूत्र: \((a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)\)।
\(18^2 = a^2 + b^2 + c^2 + 2(92) \implies 324 = a^2 + b^2 + c^2 + 184 \implies a^2 + b^2 + c^2 = 140\)।