Question

If $x+y+z=10$ and $xy+yz+zx=20$, what is the value of $x^2+y^2+z^2$?

• A. 40
• B. 60
• C. 80
• D. 50

Answer 1

The correct option is B 60

We know,

$(x+y+z{)}^2$ = $x^2+y^2+z^2+2(xy+yz+zx)$

Given,
x + y + z = 10 and xy + yz + zx = 20

$\therefore$
$(10{)}^2$ = $x^2+y^2+z^2$ + 2(20)
$\Rightarrow$ $100-40$ = $x^2+y^2+z^2$
$\Rightarrow$ $x^2+y^2+z^2$ = $60$