Question : If $a + b + c = 15$ and $a b + b c + c a = 22$ , then find the value of $a^{2} + b^{2} + c^{2}$ .
Option 1: 131
Option 2: 141
Option 3: 161
Option 4: 181

Question

Question : If $a^{3} + 3 a^{2} + 3 a = 63$ , then the value of $a^{2} + 2 a$ is:
Option 1: 22
Option 2: 19
Option 3: 15
Option 4: 8

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Answer 1

Correct Answer: 181

Solution : Given:
$a + b + c = 15$ and $a b + b c + c a = 22$
$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)$
⇒ $(15)^{2} = a^{2} + b^{2} + c^{2} + 2 (22)$
⇒ $225 = a^{2} + b^{2} + c^{2} + 44$
⇒ $a^{2} + b^{2} + c^{2} = 181$
Hence, the correct answer is 181.

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Question : If a+b+c=15 and ab+bc+ca=22, then find the value of a2+b2+c2.Option 1: 131Option 2: 141Option 3: 161Option 4: 181

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Question : If $a + b + c = 15$ and $a b + b c + c a = 22$ , then find the value of $a^{2} + b^{2} + c^{2}$ .
Option 1: 131
Option 2: 141
Option 3: 161
Option 4: 181