The integer a b satisfies the square of a b 2ab and finds a b a b

Solution: the square of a - the square of b = 2ab, the left and right sides of the equation are squared by b at the same time, (a b) 2-2(a b)-1=0, the solution is a b = 1 + root number 2 or a b = 1 - root number 2, and the division of a-b a + b is obtained.

Numerator denominator. Divide by b and the final result is root number 2-1, or -1 root number 2

If one of a and b is zero, according to a -b = 2ab, and the other is also zero, the equation is meaningless, hence ab≠0

a -b =2ab (a -b ) ab=2 a b-b a=2 let a b=t, t-1 t=2, and solve t=1 2a-b) (a+b)=(a b-1) (a b+1)=(t-1) (t+1)= -1 2

The original formula is equal to a-b multiplied by a plus b equals 2ab, a plus b = 2ab divided by a-b, a-b a plus b equals a plus b multiplied by a-b and divided by a plus b to the sum squared, a-b squared 2ab

Divide both equations by b

Find a b first and then substitute it.

ab-2a-b=5

a(b-2)-(b-2)=7

b-2)(a-1)=7

b-2=1,a-1=7

or b-2=-1, a-1=-7

or b-2 = 7, a-1 = 1

or b-2 = 7, a-1 = 1

The coarse commeticists b=3, a=8 or b=1, a=-6 or early finger b=9, a=2 or b=-5, a=0

by |2a-4|+b=1 gets:|2a-4|=1-b and |2a-4|0, so the height of 1-b 0 is the crack of the ruler b 1, and because b is a positive integer, so b=1;Sock width.

So |2a-4|=1-1=0,2a-4=0, then a=2;

So the power b of a = the power of 2 to the power of 1 = 2

If a b is an integer, then a b can only be 1 and 2, a+b = 3

A squared minus b squared equals 45

a+b) unmasked (a-b) = 45

a=23, b=22 or a=9, b=6 or a=7, b=2a=(45+1) 2 or a=(15+3) 2 or a=(9+5) 2;

b = (45-1) or b = (15-3) 2 or b = (9-5) 2

Knowing that the positive integers a and b satisfy the square of a minus the square of b is equal to 15, find the values of a and b.

a+b)(a-b)=15

Because it's a positive integer.

So. a+b=5

a-b = 3.

a=4b=1

There is also 20092009 square minus 20092008 multiplied by 20092010 you change * all to square.

The price of both commodities A and B is A yuan, due to market reasons, the price of commodity A is increased by M%, and then the price is raised by -N% for sale, and 100 pieces are sold; Commodity B first reduced the price by m%, and then reduced the price by -n% for sale, and also sold 100 pieces (where m and n are positive integers). If their purchase price is B yuan each, which of the two types of goods A and B will get the most profit?

Profit of A: [A*(1+M%)(1-N%)-B]*Profit of 100B: [A*(1-M%)(1-N%)-B]*Profit of 100A minus Profit of B.

A positive number is a large.

A negative number is a big b.

Solution: a + b +1<2a-2b

a²-2a+1+b²+2b+1<1

a-1)²+b+1)²<1

A and b are integers, (a-1) +b+1) are integers, the square term is always non-negative, and the sum of the two non-negative terms is still non-negative.

a-1) +b+1) 0, and (a-1) +b+1) <1(a-1) +b+1) =0

a-1=0b+1=0

The solution yields a=1 and b=-1

a+b=1+(-1)=0

a²=b²+23

a²-b²=23

a+b)(a-b)=23

Since a and b are positive integers, 23 can only be decomposed into 1 23 and a+b=23 and a-b=1

So a=12, b=11

Solution: Since a,b are the two real roots of the equation: (m-1)x 2+x+m 2-1=0, so: (m-1)a 2+a+m 2-1=0 (1)(m-1)b 2+b+m 2-1=0 (2)(1)-(2) obtain:

m-1)(a2-b 2)+(a-b)=0(m-1)(a-b)(a+b)+(a-b)=0 because: a+b=1 3

So: (a-b)[(m-1)*1 3+1] =0So: a-b=0, or (m-1)*1 3+1=0 When: a-b=0, a=b=1 6 After testing, m is a real number when a is not equal to b.

m-1）*1/3+1=0

So: m=-2

So, the original form is:

3x^2+x+3=0

So: x1=4 3 x2=-1

So: a=4 3 b=-1 or: a=-1, b=4 3 In summary: when: m=-2 a=4 3 b=-1 or: a=-1, b=4 3

Or: a=b=1 3

Because a = b +23 a -b =23 (a + b) * (a - b) = 23

And because they are all positive integers, a+b=23 a-b=1

Solution: a=12 b=11