lf in a triangle $A B C, ∠ B = 60^{0}$ then which of the following option is correct.

(a - b)^{2} = c^{2} - a b

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(b - c)^{2} = a^{2} - b c

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(c - a)^{2} = b^{2} + a c

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a^{2} + b^{2} + c^{2} = 2 b^{2} + a c

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Solution

The correct option is C $a^{2} + b^{2} + c^{2} = 2 b^{2} + a c$
$c o s B = \frac{a^{2} + c^{2} - b^{2}}{2 a c}$
$c o s 60 = \frac{a^{2} + c^{2} - b^{2}}{2 a c}$
$\frac{1}{2} = \frac{a^{2} + c^{2} - b^{2}}{2 a c}$
$a^{2} + c^{2} - b^{2} = a c$
$a^{2} + c^{2} + b^{2} = a c + 2 b^{2}$

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∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 + a^{2} + a^{4} & 1 + a b + a^{2} b^{2} & 1 + a c + a^{2} c^{2} 1 + a b + a^{2} b^{2} & 1 + b^{2} + b^{4} & 1 + b c + b^{2} c^{2} 1 + a c + a^{2} c^{2} & 1 + b c + b^{2} c^{2} & 1 + c^{2} + c^{4} \end{matrix} ∣ ∣ ∣ ∣ ∣ = {(a - b)}^{2} {(b - c)}^{2} {(c - a)}^{2}

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