Correct Answer - Option 2 : 1160
Given:
(r + s)2 = 49
(r – s)2 = 9
Concept:
⇒ (a + b)2 + (a – b)2 = 2(a2 + b2)
⇒ (a + b)2 - (a – b)2 = 4ab
Calculation:
According to the question,
⇒ 2(r2 + s2) = (r + s)2 + (r – s)2
⇒ 2(r2 + s2) = 49 + 9
⇒ r2 + s2 = 29 ……(1)
According to the question,
⇒ 4rs = (r + s)2 – (r – s)2
⇒ 4rs = 49 – 9
⇒ 4rs = 40 ……(2)
From (1) and (2) we get,
⇒ 4rs × (r2 + s2) = 40 × 29 = 1160