It is known that the square of 2008 (x + y) 2 is opposite to 1y-1 | of 2007 | 2, and the power of x2008-y2007 is calculated

It is known that the square of 2008 (x + y) 2 is opposite to 1y-1 | of 2007 | 2, and the power of x2008-y2007 is calculated

Don't look at the previous coefficients. Are absolute values and squares familiar? So (x + y) 2 = | 1 / 2, Y-1 | = 0, so y = 2, x = 2
2008 power of 2-2007 power of 2 = 2007 power of 2 × 2007 power of 2-2 = 2007 power of 2

It is known that x, y, Z are positive integers, and X

X + y + Zmax = 2007 + Zmax
When Z is the maximum, y is the maximum
Y = 2007-x = 2006
Z=2008+2006=4014
So x + y + Z = 2007 + 4014 = 6021
Impossible, because at least one of these three numbers is an integral multiple of 3

Known: 2 ^ x * 3 ^ y * 37 ^ z = 1998, x, y, Z are positive integers. Find the value of [(X-Y + Z) ^ 2006] ^ 2007

2^x*3^y*37^z=1998=2*3³*37
x=1,y=3,z=1,
[(x-y+z)^2006]^2007
=[(1-3+1)^2006]^2007
=[(-1)^2006]^2007
=[1]^2007
=1