(1) When a = 0, x=0, which is consistent;

(2) When a is not equal to 0, if the quadratic equation has only one solution, it is judged as 0, that is, 4-4a*a=0, and the solution is a= 1 or-1.

To sum up, a = 0, 1,-1.

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Attention! The equation ax 2+2x+a = 0 about x is a pseudo quadratic equation, so we should pay attention to the discussion of a.

2. Because of k∈R, there are two situations:

(1)k=0, x=2/3, which is consistent;

(2) If k is not equal to 0, if the quadratic equation has at most one solution, it is judged to be less than or equal to 0.

That is, 9-2*4*k is less than or equal to 0, and the solution of k is greater than or equal to 9/8.

To sum up, k is greater than or equal to 9/8 or equal to 0.

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Attention! The equation kx 2-3x+2 = 0 about x is a pseudo quadratic equation, so we should pay attention to the discussion of k.

3. When a=0 and b=0, x = 0；;

1/(√2- 1), 1/(√3-√2) can be changed to (√2+ 1) and (√3+√2).

So when a= 1 and b= 1, there is x= 1/(√2- 1), but there are no integers a and b to make x= 1/(√3-√2).

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Attention! The transformation of scores is the key!

4.x∈N, and 2 < x, so x=3, 4, 5, 6, ... because there are only three elements in the set p,

So the three elements are 3, 4 and 5, so the integer a=6.

5. According to the mutual dissimilarity of elements in the set, (1)x is not equal to 3.

(2)x is not equal to x 2-2x.

(3) x 2-2x is not equal to 3

The simultaneous solutions of the above three formulas show that x is not equal to 3 and x is not equal to 0 and x is not equal to-1.

I solved it myself for a long time! ! Don't make me busy for nothing! ! My answer is the most detailed, and there are some points for attention. I hope you can adopt it.

Study hard and wish you an early success!