Question
If $a^2+ b^2+ c^2= 50$ and $ab+bc+ ca = 47,$find $a + b + c.$
✓
Answer
$a^2+b^2+c^2=50$ and $a b+b c+c a=47 $
$ \text { Since }(a+b+c)^2=a^2+b^2+c^2+2(a b+b c+c a) $
$ \therefore(a+b+c)^2=50+2(47) $
$ \Rightarrow(a+b+c)^2=50+94=144 $
$ \Rightarrow a+b+c=\sqrt{144}= \pm 12 $
$ \therefore a+b+c= \pm 12$
$ \text { Since }(a+b+c)^2=a^2+b^2+c^2+2(a b+b c+c a) $
$ \therefore(a+b+c)^2=50+2(47) $
$ \Rightarrow(a+b+c)^2=50+94=144 $
$ \Rightarrow a+b+c=\sqrt{144}= \pm 12 $
$ \therefore a+b+c= \pm 12$
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