If a2 + b2 + c2
Question:

If $a^{2}+b^{2}+c^{2}=16$ and $a b+b c+c a=10$, find the value of $a+b+c$ ?

Solution:

We know that,

$(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2(a b+b c+c a)$

$(x+y+z)^{2}=16+2(10)$

$(x+y+z)^{2}=36$

$(x+y+z)=\sqrt{36}$

$(x+y+z)=\pm 6$

Hence, value of required expression I; (a + b + c) = ± 8

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