If x / 3 = Y / 1 = Z / 2 and XY + YZ + ZX = 99, find the value of ZX square + 9y square + 9z square?

If x / 3 = Y / 1 = Z / 2 and XY + YZ + ZX = 99, find the value of ZX square + 9y square + 9z square?

Let X / 3 = Y / 1 = Z / 2 = KX = 3ky = KZ = 2kxy + YZ + ZX = 993k * k + k * 2K + 3K * 2K = 993k ^ 2 + 2K ^ 2 + 6K ^ 2 = 9911k ^ 2 = 99K ^ 2 = 9K = ± 3x ^ 2 = 9K ^ 2 = 9 * 9 = 81y ^ 2 = k ^ 2 = 9z ^ 2 = 4K ^ 2 = 4 * 9 = 36 when k = 3, z = 6zx ^ 2 + 9y ^ 2 + 9z ^ 2 = 6 * 81 + 9 * 9 + 9 * 36 = 891 when k = 3, z = - 6zx ^ 2 + 9y ^ 2 + 9z ^ 2 = -

Math problem XY & x + y = - 2, YZ & Y + Z = 4 & 3, ZX & Z + x = - 4 & 3 find XYZ% XY + XZ + YZ

According to the known conditions, XY / (x + y) = - 2 is divided by XY on the left side of the equation to obtain: Formula 1: 1 / (1 / x + 1 / y) = - 2. Similarly, the other two known conditions can be simplified as: Formula 2: 1 / (1 / y + 1 / z) = 4 / 3, formula 3: 1 / (1 / x + 1 / z) = - 4 / 3; Formula 1 can be deformed as: 1 / x + 1 / y = - 1 / 2, formula 2 can be deformed as: 1 / y + 1 / Z

It is known that x, y and Z are positive numbers. It is proved that X of YZ + y of ZX + y of XY is greater than or equal to one of X + one of Y + one of Z

It is necessary to prove that X / YZ + Y / ZX + Z / XY > = 1 / x + 1 / y + 1 / Z
(x^+y^+z^)/xyz>=(xy+yz+zx)/xyz
x^+y^+z^>=xy+yz+zx
x^+y^+z^-xy-yz-zx>=0
Multiply both sides by two to obtain (X-Y) ^ + (Y-Z) ^ + (z-x) ^ > = 0
So established

A mathematical problem, known as x + y + Z = 1, x ^ 2 + y ^ 2 + Z ^ 2 = 2, ask XY + YZ + ZX, x ^ 3 + y ^ 3 + Z ^ 3

xy+yz+xz={（x ²+ y ²+ z ²+ 2xy+2xz+2yz）-（x ²+ y ²+ z ²）}\ 2={（x+y+z） ²- （x ²+ y ²+ z ²）}\ 2=-1\2
（x+y+z） ³= x ³+ y ³+ z ³+ 2x ² （y+z）+2y ² （x+z）+2z ² （x+y）
（x+y+z）（x ²+ y ²+ z ²）= x ³+ y ³+ z ³+ x ² （y+z）+y ² （x+z）+z ² （x+y）
x ² （y+z）+y ² （x+z）+z ² （x+y）=（x+y+z） ³- （x+y+z）（x ²+ y ²+ z ²）= 1-2=-1
x ³+ y ³+ z ³= （x+y+z）（x ²+ y ²+ z ²）- {x ² （y+z）+y ² （x+z）+z ² （x+y）}=3

If x / 3 = Y / 2 = Z / 5, the fraction XY + YZ + ZX / X ²+ y ²+ z ² be equal to?

Let X / 3 = Y / 2 = Z / 5 = K
Then x = 3k, y = 2K, z = 5K
xy+xz+yz/x^2+y^2+z^2
=(6k^2+15k^2+10k^2)/(9k^2+4k^2+25k^2)
=(6+15+10)/(9+4+25)
=31/38

4 - (3-x + 2x Square) - (2x-x square + X Cubic) 1x square of 2 - (2x square - XY + 3Y Square) - 2Y square of 3 simplification 3 (a square b-2ab) - (4a square B + 2Ab square AB) Please, just these three questions, just simplify~~

4 - (3-x + 2x Square) - (2x-x square + X Cubic)
=4-3+x-2x ²- 2x+x ²- x ³
=4-x-x ²- x ³
1X / 2 square - (2x square - XY + 3Y Square) - 2Y / 3 square
=x ²/ 2-2x ²+ xy-3y ²- 2/3y ²
=xy-3/2x ²- 3y ²- 2/3y ²
3 (a square b-2ab) - (4a square B + 2Ab square AB)
=3a ² b-6ab-4a ² b-2ab ²+ ab
=-a ² b-2ab ²- 5ab