Question : If $(a + b + c) = 13$ and $(ab + bc + ca) = 54$, find the value of $\left(a^2+b^2+c^2\right)$.
Option 1: 63
Option 2: 65
Option 3: 61
Option 4: 59
Answer (1)
21st Jan, 2024
Correct Answer: 61
Solution :
$(a + b + c) = 13$
Squaring both sides,
$(a^2+b^2+c^2)+2(ab + bc + ca)=169$
⇒$(a^2+b^2+c^2)+108=169$
⇒ $(a^2+b^2+c^2)=61$
Hence, the correct answer is 61.
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