Question

if X + Y + Z is equal to 10 and X square + Y square + Z square is equal to 40 then xy + y z + z x is equal to

Answer 1

Answer:

XY + YZ + ZX = 30

Step-by-step explanation:

X + Y + Z = 10

X² + Y² + Z² = 40

X + Y + Z = 10

X + Y = 10-Z

Squaring both sides

X² + Y² + 2XY = 100 + Z² - 20Z

similarly

Y² + Z² + 2YZ = 100 + X² - 20X

X² + Z² + 2XZ = 100 + Y² - 20Y

Adding all three

2(X² + Y² + Z²) + 2(XY + YZ + ZX) = 300 + (X² + Y² + Z²) - 20(X + Y + Z)

=> 2(XY + YZ + ZX) = 300 -  (X² + Y² + Z²) - 20(X + Y + Z)

=>  2(XY + YZ + ZX) = 300 -  40 - 20(10)

=> 2(XY + YZ + ZX)  = 60

=> XY + YZ + ZX = 30