Mohammed 23
New member
- Joined
- Nov 5, 2020
- Messages
- 14
Hi Mohammed. Your approach is okay. Using algebra to eliminate variables or to solve pairs of equations for the same expression is a good start. When you find a certain variable or expression repeated, you can proceed with substitutions, to make progress.… I don’t think I've taken the right approach …
Well I don’t know if it’s necessary that a b c and d need to be integers , it’s not mentioned in the question and was just an assumption I made . But , the final answer of a+b+c+d needs to be an integer for sureBy any chance did the problem say that a, b, c and d are integers. If yes, then why not tell us? In no, then why when a product of two factors equal 13 must the factors be 1 and 13. Why not 11sqrt3 and 13/911sqrt3 ?
Yes I know they need not be integers , but I assumed so that it’s easier to find out the individual values if they are taken as integers . The final sum however needs to be an integer . I haven’t been able to get any equation which helps me eliminate a variable yet .Hi Mohammed. Your approach is okay. Using algebra to eliminate variables or to solve pairs of equations for the same expression is a good start. When you find a certain variable or expression repeated, you can proceed with substitutions, to make progress.
However, some of your work shows that you're assuming {a,b,c,d} are Integers. They are not Integers. (If you were expecting Integer solutions, then please check to be sure you copied the exercise correctly.)
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Actually, I don’t think all this is needed .I don’t feel we need to find out individual values to find the sum of all the valuesSome subtraction on the left side are wrong. Go back and fix them.
Oh thanks , I think substitution is the only way then . Sorry for taking so much of your time actually, it is to be done by hand , without use of calculatorHi Mohammed. I played around with the system as posted, using paper & pencil. First, I solved for {b,c,d} each in terms of a. Substitution then yielded:
(679/36)a + (14√142/9)a + 13√142/9 = -149/36
I obtained two solutions, for a. (One of them turned out to be extraneous, but I didn't realize it until later.)
At that point, I'd spent nearly two hours, so I finished the back-substitution using a computer.
I would hope there's a shortcut that I missed, if that system is supposed to be solved by hand.
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No need to apologize. The work that I did was for fun.… Sorry for taking so much of your time
thanks a ton . I wanted to know how to solve it very badly . Thanks a lot for your timeWell, darn it all. I've got more than a dozen sheets of paper with over 100 equations, but I can't figure out why I'd scribbled:
ab + cd = -27
If we can justify that, then here's how it goes from there.
We add bc to each side:
ab + bc + cd = bc - 27
Now, we know that bc - 27 = -a - d, so we have:
ab + bc + cd = -a - d
And we know that da = 17 - b - c, so adding the respective sides gives:
ab + bc + cd + da = -a - d - b - c + 17
You'd written:
ab + bc + cd + da + 2(a + b + c + d) = 87
Therefore:
-a - b - c - d + 17 + 2(a + b + c + d) = 87
or
2(a + b + c + d) - (a + b + c + d) = 70
My brain is a bit fried; I'll try to revisit my papers later.