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If a + b + c = 75 and ab + bc + ca = 216. Find the value of a2 + b2 + c2 = ?

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If a + b + c = 75 and ab + bc + ca = 216. Find the value of a2 + b2 + c2 = ?
1). 5194
2). 5191
3). 5193
4). 5192


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Answered by on | Votes 0 |

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

⇒ (75)2 = a2 + b2 + c2 + 2 (216)

⇒ 5625 = a2 + b2 + c2 + 432

⇒ a2 + b2 + c2 = 5625 – 432

∴ a2 + b2 + c2 = 5193

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