Question

Question 30
if $a+b+c=9$ and $ab+bc+ca=26$, find $a^2+b^2+c^2$.

Answer 1

Given,
$a+b+c=9$ and $ab+bc+ca=26$ …..(i)
Now,
a + b + c = 9
On squaring both sides, we get,
$(a+b+c{)}^2=(9{)}^2$
$\Rightarrow a^2+b^2+c^2+2ab+2bc+2ca=81$
$[Usingtheidentity,(a+b+c{)}^2=a^2+b^2+c^2+2ab+2bc+2ca]$
$\Rightarrow a^2+b^2+c^2+2(ab+bc+ca)=81$
$\Rightarrow a^2+b^2+c^2+2\left(26\right)=81$ [from eq.(i)]
$\Rightarrow a^2+b^2+c^2=81–52=29$