It is known that 2006 (X-Y) + 2007 (Y-Z) + 2008 (z-x) = 02006 ^ 2 (X-Y) + 2007 ^ 2 (Y-Z) + 2008 ^ 2 (z-x) = 2008 Finding z-x

It is known that 2006 (X-Y) + 2007 (Y-Z) + 2008 (z-x) = 02006 ^ 2 (X-Y) + 2007 ^ 2 (Y-Z) + 2008 ^ 2 (z-x) = 2008 Finding z-x

(x+y-z)/z=(y+z-x)/x=(z+x-y)/y
[x+y]/z-1=[y+z]/x-1=[z+x]/y-1
[x+y]/z=[y+z]/x=[z+x]/y
Let [x + y] / z = [y + Z] / x = [Z + x] / y = K
k[x+y+z]=[(y+z)/x]*x+[(z+x)/y]*y+[(x+y/z]*z=2[x+y+z]
k=2
(x+y)(y+z)(z+x)/xyz
=(x+y)/z*(y+z)/x*(z+x)/y=2*2*2=8

If a = 20052006, B = 20062007, C = 20072008, then the largest of a, B, C is______ The smallest is______ ．

There is such a rule: true fraction numerator denominator at the same time plus an equal number, the score value will become larger, so it is easy to compare the size. The largest is C, the smallest is a; so the answer is: C, a

It is known that the square of 2007 (x + y) is opposite to 2008 1 / 2y-1
(1) Find the value of X and Y (2) calculate the 2007 power of X + 2008 power of Y

1) ∵ (x + y) ^ 2 > 0 ∵ 2007 * (x + y) ^ 2 > 0 ∵ 1 / 2y-1 ∵ 0 ∵ 2008 * (1 / 2y-1 ∵ 0 ∵ they can't be opposite numbers, they can only be both sides = 0 ∵ x + y = 0, 1 / 2y-1 = 0, x = - 2, y = 2 ∵ (- 2) ^ 2007 + 2 ^ 2008 = - 2 ^ 2007 + 2 ^ 2008 = - 2 ^ 2007 + 2 * 2 ^ 2007 = 2 ^ 2007