Question:
If \((x + y)^2 = 144\) and \(xy = 15\), then find \(x^2 + y^2\).
यदि \((x + y)^2 = 144\) और \(xy = 15\) है, तो \(x^2 + y^2\) का मान ज्ञात कीजिए।
Options:
- 114
- 115
- 116
- 118
- 114
- 115
- 116
- 118
Correct Answer: a)
Explanation:
Using the algebraic expansion \((x + y)^2 = x^2 + y^2 + 2xy\):
\(144 = x^2 + y^2 + 2(15) \implies x^2 + y^2 = 144 – 30 = 114\).
बीजगणितीय सर्वसमिका \((x + y)^2 = x^2 + y^2 + 2xy\) का प्रयोग करने पर:
\(144 = x^2 + y^2 + 2(15) \implies x^2 + y^2 = 144 – 30 = 114\)।