Question

$a + b - c = 5 \: and \: {a}^{2} + {b}^{2} + {c}^{2} = 29 \: find \: ab - bc - ca$
plz tell the answer for this....​

Answer 1

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$( a+b+c) = 5 \\square \: on \: both \: side \\ {( a+b+c)}^{2} = {5}^{2} \\ {a}^{2} + {b}^{2} + {c}^{2} + 2(ab - bc - ca) = 25$

${a}^{2} + {b}^{2} + {c}^{2} = 29$

Put in eq and let (ab -bc-ca) =x

$29 + 2x = 25 \\ 2x = 25 - 29 \\ 2x = - 4 \\ x = - 2 \\ (ab - bc - ca )= (- 2) \: \: \: ans...$

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