Question

if x+y+z= 10 and x y+y z +z x=30, then find value of x power 2 + y power 2 + z power 2​

Answer 1

Answer:

40

Step-by-step explanation:

x+y+z=10 .......(given)

squaring on both sides,we get :-

(x+y+z) ^2=10^2...... equation 1

since, we know that,

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

therefore,

x^2+y^2+z^2+2(xy+yz+zx) =100 ........from equation 1

but , xy+yz+zx=30........(given)

therefore,

x^2+y^2+z^2+2(30)=100

x^2+y^2+z^2+60=100

x^2+y^2+z^2=100-60

x^2+y^2+z^2=40

Therefore, answer :- x^2+y^2+z^2=40