Quantitative Reasoning

Miscellaneous

Easy

If : $a + b + c = 14$ and $a^2 + b^2 + c^2 = 96$ , then $(ab + bc + ca)$ is

✅ Correct Option: 2

Given:

$a + b + c = 14$

$a^2 + b^2 + c^2 = 96$

Using the algebraic identity:

$(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)$

Substituting the given values:

$(14)^2 = 96 + 2(ab + bc + ca)$

$196 = 96 + 2(ab + bc + ca)$

$196 - 96 = 2(ab + bc + ca)$

$100 = 2(ab + bc + ca)$

$ab + bc + ca = \dfrac{100}{2}$

$ab + bc + ca = 50$

Therefore, $(ab + bc + ca) = 50$

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If : a+b+c=14a + b + c = 14a+b+c=14 and a2+b2+c2=96a^2 + b^2 + c^2 = 96a2+b2+c2=96, then (ab+bc+ca)(ab + bc + ca)(ab+bc+ca) is