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if a+b+c=9 and ab+bc+ca=26 find a2+b2+c2

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if a+b+c=9 and ab+bc+ca=26

find a²+b²+c²

Posted by Ashu Shrivas 8 years, 6 months ago

CBSE > Class 09 > Mathematics

1 answers

Rashmi Bajpayee 8 years, 6 months ago

We know that {tex}{\left( {a + b + c} \right)^2} = {a^2} + {b^2} + {c^2} + 2ab + 2bc + 2ca{/tex}

{tex}\Rightarrow{/tex} {tex}{a^2} + {b^2} + {c^2} = {\left( {a + b + c} \right)^2} - 2ab - 2bc - 2ca{/tex}

{tex}\Rightarrow{/tex} {tex}{a^2} + {b^2} + {c^2} = {\left( {a + b + c} \right)^2} - 2\left( {ab + bc + ca} \right){/tex}

Putting the given values of a + b + c and ab + bc + ca, we get

{tex}\Rightarrow{/tex} {tex}{a^2} + {b^2} + {c^2} = {\left( 9 \right)^2} - 2\left( {26} \right){/tex}

{tex}\Rightarrow{/tex} {tex}{a^2} + {b^2} + {c^2} = 81 - 52 = 29{/tex}

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