Question

if X + Y + Z is equal to 10 and square + Y square + b square is equal to 40 then find three of xy + y z + zx​

Answer 1

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

Answer 2

Answer:

Step-by-step explanation:

XY+YZ+ZX=30