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if a +b+c=9 and ab+bc+ca=26,find `a^(2)+b^(2)+c^(2).` |
Answer» Given `a+b+c= 9 and ab+bc+ca=26 ` Now `a+b+c=9` On squaring both sides , we get `(a+b+c)^(2)=(9)^(2)` `implies a^(2)+b^(2)+c^(2)+2ab+2bc+2ca=81` [using identity,`(a+b+c)^(2) =a^(2)+b^(2)+c^(2)+2ab+2bc+2ca`] ` implies a^(2)+b^(2)+c^(2) +2(ab+bc+ca)=81` ` implies a^(2) +b^(2)+c^(2)+2(26)=81` ` implies a^(2)+b^(2)+c^(2)=81-52=29` |
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