Given a = 2x2-3x, B = x2-x + 1, find the value of algebraic expression a-3b when x = - 1

Given a = 2x2-3x, B = x2-x + 1, find the value of algebraic expression a-3b when x = - 1

∵A=2x2-3x，B=x2-x+1，
∴A-3B
=（2x2-3x）-3（x2-x+1）
=2x2-3x-3x2+3x-3
=-x2-3，
When x = - 1, the original formula = - (- 1) 2-3 = - 4

Given that 3x-4y-z = 0, 2x + y-8z = 0, then the algebraic formula x2 + Y2 + Z2 xy+yz+2zx=______ .

∵3x-4y-z=0，
∴z=3x-4y，
Substituting 2x + y-8z = 0 leads to y = 2
3x，
And then substituting it into Z = 3x-4y, we get z = 1
3x，
The algebraic formula x2 + Y2 + Z2
xy+yz+2zx=x2+4
9x2+1
9x2  
x•2
3x+2
3x•1
3x+2x•1
3x =1．
So the answer is: 1

Given that 3x-4y-z = 0, 2x + y-8z = 0, then the algebraic formula x2 + Y2 + Z2 xy+yz+2zx=______ .

∵3x-4y-z=0，
∴z=3x-4y，
Substituting 2x + y-8z = 0 leads to y = 2
3x，
And then substituting it into Z = 3x-4y, we get z = 1
3x，
The algebraic formula x2 + Y2 + Z2
xy+yz+2zx=x2+4
9x2+1
9x2  
x•2
3x+2
3x•1
3x+2x•1
3x =1．
So the answer is: 1

Given {3x-4y-z = 0, find the value 2x + Y-8 = 0 of x ^ 2 + y ^ 2 + Z ^ 2 / XY + YZ + 2zx

From 3x-4y-z = 0, z = 3x-4y
From 2x + y-8z = 0, y = 8z-2x 4
④ X = 3Z (5) is obtained by substituting ③
y=2z
Put x, y in
(x^2+y^2+z^2)/(xy+yz+2zx)
=(9z^2+4z^2+z^2)/(6z^2+2z^2+6z^2)
=(14z^2)/(14z^2)
=1

Given that 3x-4y-z = 0, 2x + y-8z = 0, then the algebraic formula x2 + Y2 + Z2 xy+yz+2zx=______ .

∵3x-4y-z=0，
∴z=3x-4y，
Substituting 2x + y-8z = 0 leads to y = 2
3x，
And then substituting it into Z = 3x-4y, we get z = 1
3x，
The algebraic formula x2 + Y2 + Z2
xy+yz+2zx=x2+4
9x2+1
9x2  
x•2
3x+2
3x•1
3x+2x•1
3x =1．
So the answer is: 1

If x + y + Z = 0 and X, y, Z are not equal to each other, find x ^ 2 / (2x ^ 2 + YZ) + y ^ 2 / (2Y ^ + XZ) + Z ^ 2 / (2Z ^ 2 + XY). Online, etc

Suppose x = 0, y = 1, z = - 1
Then:
x^2/(2x^2+yz)+y^2/(2y^+xz)+z^2/(2z^2+xy)
=0/（0-1）+1/（2-0）+（-1）²/（2+0）
=0+1/2+1/2
=1

Given XYZ = 1. X2 + Y2 + Z2 = 16. Find the value of 1 / XY + 2Z + 1 / YZ + 2x + 1 / XZ + 2Y

If it is XYZ = 1, x + y + Z = 2, x ^ 2 + y ^ 2 + Z ^ 2 = 16, finding 1 / XY + 2Z + 1 / YZ + 2x + 1 / XZ + 2Y should be the original formula = (1 / XY + 2Z) + (1 / YZ + 2x) + (1 / XZ + 2Y) general partition = (Z + 2xyz) / XYZ + (x + 2xxyz) / XYZ + (y + 2xyyz) / XYZ simplification = (x + y + Z + 2xyz (x + y + Z)

Given that 2x-3y + Z = 0,3x-2y-6z = 0 and XYZ ≠ 0, find the value of (x squared + y squared + Z squared) / (XY + YZ + XZ)

x = 4/3 y
z = 1/3 y
(x²+y²+z²)/(xy+yz+xz)
=(16/9y²+y²+1/9y²)/(4/3y²+1/3y²+4/9y²)
=(26/9)/(19/9)
=26/19

Given x + y + Z = a, XY + YZ + XZ = B, find the value of X * x + y * y + Z * Z

(X+Y+Z)^2=x^2+y^2+z^2+2(xy+yz+xz)
=a^2=x^2+y^2+z^2+2b
So x ^ 2 + y ^ 2 + Z ^ 2 = a ^ 2-2b

Given x + y + Z = 2, XY + YZ + XZ = - 5, find the value of x 2 + y 2 + Z 2

Square x + y + Z = 2 to get: (x + y + Z) 2 = x2 + Y2 + Z2 + 2XY + 2yz + 2zx = 4,
Substituting XY + YZ + XZ = - 5 into: x2 + Y2 + Z2 = 14