Question

if X + Y + Z is equal to 10 and X square + Y square + Z square is equal to 40 find X Y + y z + exact and x cube + y cube + Z cube minus 3 x y z​

Answer 1

Answer:

hope it helps

Step-by-step explanation:

hey mate here is ur answer

Answer 2

xy+yz+zx=30

x³+y³+z³-3xyz=100

Step-by-step explanation:

Given:

x+y+z=10

x²+y²+z²=40.

We know that

(a+b+c)²=a²+b²+c²+2(ab+bc+ca)

x+y+z=10

Take square on both sides

⇒(x+y+z)²=10²

⇒x²+y²+z²+2(xy+yz+zx)=100

Substituting the value x²+y²+z²=40

⇒40+2(xy+yz+zx)=100

⇒2(xy+yz+zx)=100-40

⇒2(xy+yz+zx)=60

Cross multiplying

⇒xy+yz+zx=30

We know that

x³+y³+z³=(x+y+z)(x²+y²+z²-xy-yz-zx)+3xyz

⇒x³+y³+z³-3xyz=(x+y+z)(x²+y²+z²-(xy+yz+zx))

Substituting the known values

⇒x³+y³+z³-3xyz=10(40-30)

⇒x³+y³+z³-3xyz=10(10)

⇒x³+y³+z³-3xyz=100

Learn More:

If X + Y + Z is equal to 1, xy + yz plus zx is equal to -1 and x y z is equal to -1, find the value of x cube + y cube + Z cube

https://brainly.in/question/10750732