Question

# If $$a + b + c = 9$$ and $$ab + bc + ca = 26$$, then find $$a^{2} + b^{2} + c^{2}$$.

A
26
B
27
C
28
D
29

Solution

## The correct option is D $$29$$Given, $$a+b+c=9$$ and $$ab+bc +ca=26$$.We know, $$(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2ab +2bc+2ca$$$$\Rightarrow (a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2(ab+bc+ca)$$.Putting the values here, we get,$$(9)^{2}=a^{2}+b^{2}+c^{2}+2(26)$$$$\Rightarrow 81=a^{2}+b^{2}+c^{2}+52$$$$\Rightarrow a^{2}+b^{2}+c^{2}=81-52=29$$.Hence, option $$D$$ is correct.Mathematics

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