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 If (r + s)2 = 49 and (r – s)2 = 9, what is the value of 4rs × (r2 + s2)?
1. 1360
2. 1160
3. 1140
4. 1250

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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

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