Math, asked by kka83, 5 months ago

plz help me????????? ​

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Answered by BrainlyEmpire
201

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\textbf{Hey there}!!

\textbf{Solution}:

Taking L.H.S:

=  \begin{vmatrix}1&a&a^{2} \\ \\ 1&b&b^{2}\\ \\ 1&c&c^{2} \end{vmatrix}

Applying R_{1}R_{1} - R_{2}

=  \begin{vmatrix}0&a - b&a^{2} - b^{2} \\ \\ 1&b&b^{2}\\ \\ 1&c&c^{2} \end{vmatrix}

Applying R_{2}R_{2} - R_{3}

= \begin{vmatrix}0&a - b&a^{2} - b^{2} \\ \\ 0&b - c&b^{2} - c^{2}\\ \\ 1&c&c^{2} \end{vmatrix}

Applying C_{1}C_{1} + C_{2}

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

Taking ( a - b )( b - c ) common from

R_{1} and R_{2} respectively.

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

Applying C_{1}C_{1} - C_{2}

= ( a - b ) ( b - c )\begin{vmatrix}0&1&a + b \\ \\ 0&1&b + c\\ \\ 1 &c&c^{2} \end{vmatrix}

Expanding C_{1}

= ( a - b) (b - c ) 1[ b + c - a - b ]

= ( a - b ) ( b - c ) [b + c - a - b]

= ( a - b ) ( b - c ) ( c - a ) =R.H.S

#Be Brainly.

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