First of all, it must be clear that the number in the root sign is either positive or zero, so when √A+√B=0, both A and B are zero. (Because if A is positive, then √A is positive, and to satisfy √A+√B=0, then √B must be negative, and √B cannot be negative, so both A and B are zero. )

The absolute value of 1 ∫(ax-2y-4) and the root sign (2x+4) are reciprocal.

∴(ax-2y-4) Absolute value+radical sign (2x+4)=0.

The absolute value of ∵(ax-2y-4) is ≥0, and the root sign (2x+4) is ≥ 0.

∴ (absolute value of ax-2y-4) =0, and the root sign (2x+4)=0.

X=-2

Because x and y are reciprocal.

∴y=2

∴a*-2-2*4=0

∴a=-4

2.y=√ 1-2x+√(x- 1)？ +√2x- 1，

It can be noted that √ 1-2x and √2x- 1,

√2x- 1=√ -( 1-2x)

So √ 1-2x and √2x- 1 are reciprocal.

(The opposite number is either positive, negative or zero. It can't be positive, so it's all zero. )

So 1-2x=0 and X= 1/2.

Substituting X= 1/2 into the original formula, you can get Y= 1/2.

So the arithmetic square root of X+Y = 1.

3.

a- 1=0，ab-2=0

a= 1，ab=2

So b=2 and a=2.

Then the original formula =11* 2+1/2 * 3+1/3 * 4+...+1/2010 * 20/kloc-.

= 1- 1/2+ 1/2- 1/3+ 1/3- 1/4+……+ 1/20 10- 1/20 1 1

= 1- 1/20 1 1

=20 10/20 1 1

I am exhausted. . . . .