Question:
If \(a^2 + b^2 + c^2 = 180\) and \(ab + bc – ca = 44\), then find the value of \((a – b + c)^2\).
यदि \(a^2 + b^2 + c^2 = 180\) और \(ab + bc – ca = 44\) है, तो \((a – b + c)^2\) का मान ज्ञात कीजिए।
Options:
- 68
- 24
- 56
- 92
- 68
- 24
- 56
- 92
Correct Answer: d)
Explanation:
Expansion: \((a – b + c)^2 = a^2 + b^2 + c^2 – 2ab – 2bc + 2ca = (a^2 + b^2 + c^2) – 2(ab + bc – ca)\).
\((a – b + c)^2 = 180 – 2(44) = 180 – 88 = 92\).
\((a – b + c)^2 = a^2 + b^2 + c^2 – 2(ab + bc – ca)\)
\(= 180 – 2(44) = 180 – 88 = 92\)। अतः विकल्प (d) सही है।