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Question -

If a + b + c = 9 and  ab + bc + ca = 23, then a2 + b2 + c2 =
(a) 35
(b) 58
(c) 127
(d) none of these



Answer -

a + b + c = 9, ab + bc + ca = 23
Squaring,
(a + b+ c) = (9)2
a2 + b2 + c2 + 2 (ab + bc+ ca) = 81
a2 +b2 + c2 + 2 x 23 = 81
 a2 + b2+ c2 + 46 = 81
 a2 + b2+ c2 = 81 – 46 = 35  (a)

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