if a +b+c=9 and ab+bc+ca=26,find `a^(2)+b^(2)+c^(2).`

Options

A. 27
B. 28
C. 29
D. -29

Answer

C

Explanation

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`