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Question -

If a + b + c = 9 and ab + bc + ca = 40, find a2 + b2 + c2.



Answer -

a + b + c = 9, ab + bc + ca = 40
Squaring both sides,
(a + b + c)2 = (9)2
a2 + b2 + c2 + 2{ab + bc+ ca)  = 81
a2 +b2 + c2 + 2 x 40 = 81
 a2 + b2 + c2 + 80 = 81
a2 + b2 + c2 = 81 – 80 = 1

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