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