1.

If a + b + c = 9 and ab + be + ca = 26, find a2 + b2 + c2

Answer»

Given that a + b + c = 9 

Squaring on both sides, (a + b + c)2 = 92 

⇒ a2 + b2 + c2 + 2 (ab + be + ca) = 81 

⇒ a2 + b2 + c2 = 81 – 2 (ab + be + ca) (by problem) 

= 81 – 2 x 26 

= 81 – 52 = 29



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