Hi:
I was wondering how I would even start to solve a problem like this.
Solve for x1, x2, x3, and x4:
x1x2+x1+x2=524
x2x3+x2+x3=146
x3x4+x3+x4=104
Thanks,
Manny
I took a crack at it but did not get far.
I also have spent an unreasonable amount of time trying it.
I even went so far as to run an old-fashioned 1970ish BASIC program
10 FOR A = -25 TO 35
20 FOR B = -25 TO 35
30 FOR C = -25 TO 35
40 FOR D = -25 TO 35
50 IF ((A*B+A+B=514) AND (B*C+B+C=146) AND (C*D+C+D=104)) THEN PRINT A,B,C,D
60 NEXT D
70 NEXT C
80 NEXT B
90 NEXT A
It found no integer solutions to your problem in the domain from -25 to + 35
I used A,B,C, and D for your variables
X1,X2,....
Hi Manny,
To solve this problem, you can use a method called factoring by grouping. Factoring by grouping is a technique used to factor quadratic expressions, such as the ones you have in your equations.
Let's start with the first equation:
x1x2 + x1 + x2 = 524
To simplify this equation, we can group the terms together:
x1(x2 + 1) + 1(x2 + 1) = 524
Now, notice that we have a common factor of (x2 + 1). We can then factor that out:
(x2 + 1)(x1 + 1) = 524
Now that we have factored the left side of the equation, we can do the same for the other two equations:
x2x3 + x2 + x3 = 146
(x3 + 1)(x2 + 1) = 146
x3x4 + x3 + x4 = 104
(x4 + 1)(x3 + 1) = 104
Now we have three equations in the form (A)(B) = C, where A, B, and C are known numbers. To solve for x1, x2, x3, and x4, we need to find the values of A, B, and C.
In the first equation, A is (x2 + 1), B is (x1 + 1), and C is 524. In the second equation, A is (x3 + 1), B is (x2 + 1), and C is 146. In the third equation, A is (x4 + 1), B is (x3 + 1), and C is 104.
Now we can set up a system of equations:
(x2 + 1)(x1 + 1) = 524 -> Equation 1
(x3 + 1)(x2 + 1) = 146 -> Equation 2
(x4 + 1)(x3 + 1) = 104 -> Equation 3
To solve this system of equations, you can use various methods such as substitution, elimination, or matrices. However, without further information or relationships between the variables, it is not possible to find unique solutions to the equations.
I hope this explanation helps you in tackling the problem. If you have any further questions, feel free to ask!