1. (x square + x) square + (x + 1) square + x 2, X fourth power + 9x square + 25 3. Finding the nonnegative integer solution of the equation xy-x + y-4 = 0 4. No matter what value x and Y take, does the polynomial 2x square - 4xy + 5Y square - 12Y + 13 have the minimum value? If there is a request for the minimum value ratio, point out the value of X and y at this time

1. (x square + x) square + (x + 1) square + x 2, X fourth power + 9x square + 25 3. Finding the nonnegative integer solution of the equation xy-x + y-4 = 0 4. No matter what value x and Y take, does the polynomial 2x square - 4xy + 5Y square - 12Y + 13 have the minimum value? If there is a request for the minimum value ratio, point out the value of X and y at this time

1, sort out y = (4 + x) / (1 + x) = 1 + 3 / (1 + x), so to make y an integer, 1 + X is the divisor of 3, 1,3, corresponding to X is 0,2, bring in to find y
In order to minimize x = y = 2, the minimum is 1

The square of 25X in 4 minus 9 equals the square of 0 x plus 8x plus 15 = 0

（1） 25 (x ^ 2) / 4-9 = 0, 25 (x ^ 2) / 4 = 9 by solving the shift term, x ^ 2 = 36 / 25 by multiplying both sides by 4 / 25, and x = 6 / 5 by square root
（2） X ^ 2 + 8x + 15 = 0, factorization (x + 3) (x + 5) = 0, x = - 3 or - 5

Let a square + B square-4a + 2B + 5 = 0. Find the value of (root a + b) (root a-b)

a²＋b²－4a＋2b＋5=0
(a²－4a＋4)＋(b²＋2b＋1)=0
(a－2)²＋(b＋1)²=0
Then:
A-2 = 0 and B + 1 = 0
A = 2, B = - 1
Then:
[√(a＋b)]×[√(a－b)]=√(a²－b²)=√3

Square of 4A - square of B + 2b-1 =?

4a²-b²+2b-1=（2a）²-（b²-2b+1）=（2a）²-（b-1）²=（2a+b-1）（2a-b+1）