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Let a + b + c = 13; a2 + b2 + c2 = 69. Then ab + bc + ca = ? 
1. 20
2. 30
3. 40
4. 50

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Correct Answer - Option 4 : 50

Given

a + b + c = 13; a2 + b2 + c2 = 69.

Formula used

(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

Calculation

(a + b + c)2 = 132 = 169

⇒ 169 = 69 + 2(ab + bc + ca)

⇒ (ab + bc + ca) = (169 - 69)/2

⇒  (ab + bc + ca) = 50

∴ The value of (ab + bc + ca) is 50

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