Question:
If a + b + c = 9 and ab + bc + ca = 26, find a2 + b2 +c2.
Solution:
Given. $a+b+c=9$ and $a b+b c+c a=26$ ...(i)
Now, $\quad a+b+c=9$
On squaring both sides, we get
$(a+b+c)^{2}=(9)^{2}$
$\Rightarrow \quad a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a=81$
[using identity, $\left.(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a\right]$
$\Rightarrow \quad a^{2}+b^{2}+c^{2}+2(a b+b c+c a)=81$
$\Rightarrow \quad a^{2}+b^{2}+c^{2}+2(26)=81$ [from Eq. (i)]
$\Rightarrow \quad a^{2}+b^{2}+c^{2}=81-52=29$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.