MCQ
If $a + b + c = 9$ and $ab + bc + ca = 23,$ then $a^2+b^2+c^2=$
- ✓$35$
- B$58$
- C$127$
- DNone of these.
✓
Answer
Correct option: A.
$35$
We know that $(a+b+c)^2=a^2+b^2+c^2+2(a b+b c+c a)$
Here, $a+b+c=9, a b+b c+c a=23$
Thus, we have
$(9)^2=a^2+b^2+c^2+2(23)$
$81=a^2+b^2+c^2+46$
$a^2+b^2+c^2=81-46$
$a^2+b^2+c^2=35$
Hence, correct option is $(a).$
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