Simplify first and then evaluate: the third power of - 2Y + (the second power of 3xy - the square of x y) - 2 (the square of XY - the third power of Y), where the absolute value of (2x-2) + (y + 1) square = 0

Simplify first and then evaluate: the third power of - 2Y + (the second power of 3xy - the square of x y) - 2 (the square of XY - the third power of Y), where the absolute value of (2x-2) + (y + 1) square = 0

Absolute value of (2x-2) + (y + 1) squared = 0
Then 2x-2 = 0, y + 1 = 0
Then x = 1, y = - 1
- the third power of 2Y + (the second power of 3xy - the square of X, y) - 2 (the square of XY - the third power of Y),
=-2y ³+ 3xy ²- x ² y-2xy ²+ y ³
=-y ³+ xy ²- x ² y
=1+1+1
=3

Simplified evaluation: - XY (x2y5-xy3-y), where XY2 = - 2

Original formula = - x3y6 + x2y4 + XY2 = (- XY2) 3 + (XY2) 2 + XY2 = 8 + 4-2 = 10

Simplified evaluation: given x + y = 2, xy = 0.75, find the 3rd power of X, y + the 3rd power of XY + the 2nd power of 2x, and the 3rd power of Y

X ^ 3Y + XY ^ 3 + 2x ^ 2Y ^ 3 = XY (x ^ 2 + y ^ 2 + 2XY ^ 2) = XY [(x + y) ^ 2 + 2XY ^ 2-2xy] = XY [(x + y) ^ 2 + 2XY (Y-1)] = (3 / 4) [4 + 3 (Y-1) / 2] = 3 + 9 (Y-1) / 8 = 15 / 8 + 9y / 8x + y = 2 xy = 3 / 4x, y is two (2x-1) (2x-3) = 0x1 = 1 / 2 x2 = 3 / 2 of equation 4x ^ 2-8x + 3 = 0, that is, the value of Y is 1 / 2 or 3 /

XY + YZ + ZX = 1, find x √ YZ + y √ ZX + Z √ XY Is less than or equal to

This question examines the maximum inequality:
A + B ≥ 2 √ AB if and only if a = B, take the equal sign
x√yz+y√zx+z√xy
≤x(y+z)/2+y(z+x)/2+z(x+y)/2
If and only if y = Z, z = x, x = y, i.e. x = y = Z, take the equal sign, so:
x√yz+y√zx+z√xy
≤(xy+xz+yz+xy+xz+yz)/2
=xy+yz+xz
=1
Therefore:
X √ YZ + y √ ZX + Z √ XY ≤ 1, when x = y = Z, take the equal sign

x ³+ y ³+ z ³- Why is 3xyz equal to (x + y + Z) (x) ²+ y ²+ z ²- xy-yz-xz)

x ³+ y ³+ z ³- 3xyz=(x+y) ³- 3x ² y-3xy ²+ z ³- 3xyz=(x+y) ³+ z ³- (3x ² y+3xy ²+ 3xyz)=(x+y+z)[(x+y) ²- (x+y)z+z ²]- 3xy(x+y+z)=(x+y+z)[(x+y) ²- (x+y)z+z ...

Given x + y + Z = 2, XY + YZ + ZX = - 5, find X ²+ y ²+ z ² Value of

(x+y+z)^2=4
x^2+y^2+z^2+2xy+2xz+2yz=4
x^2+y^2+z^2+2(-5)=4
x^2+y^2+z^2=14