If a + b + c = 10 and ab + bc + ca = 24, then the value of
$a^{2} + b^{2} + c^{2} i s$ .

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Solution

The correct option is D 52
Given: a + b + c = 10 and ab + bc + ca = 24
Using the identity:
$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)$
$(10)^{2} = a^{2} + b^{2} + c^{2} + 2 \times 24$
$100 = a^{2} + b^{2} + c^{2} + 48$
$a^{2} + b^{2} + c^{2} = 100 - 48 = 52$

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