Question

if $x+y+z=11$ and $xy+yz+zx=42$ then the value of $x^2+y^2+z^2$ is:

• A. 41
• B. 37
• C. 39
• D. 43

Answer 1

Answer:

B. 37

$(x+y+z)^2=x^2+y^2+z^2+2(xy+yx+xz)$

$(x+y+z)^2=11^2$

$x^2+y^2+z^2+2(xy+yx+xz)=121$

$x^2+y^2+z^2+2(42)=121$

$x^2+y^2+z^2+84=121$

$x^2+y^2+z^2=121-84$

$x^2+y^2+z^2=37$