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2. Polynomials
hard
જો $a+b+c=9$ અને $a b+b c+c a=26,$ તો $a^{2}+b^{2}+c^{2}$ શોધો:
A
$81$
B
$29$
C
$52$
D
$26$
Solution
We have that
$(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2 a b+b c+2 c a$
$\Rightarrow(a+b+c)^{2}=\left(a^{2}+b^{2}+c^{2}\right)+2(a b+b c+c a)$
$\Rightarrow 9^{2}=\left(a^{2}+b^{2}+c^{2}\right)+2(26)$
[Putting the value of $a+b+c$ and $a b+b c+c a]$
$\Rightarrow 81=\left(a^{2}+b^{2}+c^{2}\right)+52$
$\Rightarrow\left(a^{2}+b^{2}+c^{2}\right)=81-52=29$
Standard 9
Mathematics
