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Winter vacation homework Mathematics in Grade Two (East China Normal University Edition)
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. . . . .