Can you please chk where i have made a mistake???

Question

I borrowed $4000 and after few days I again borrowed $2000 .When the other person asked me for the money
Question Details: I said
,
" the sum of 4000 and 2000 is equal to zero, so I do
not have
any balance to pay".

and i explained it with the algebric formulae " let a = 4000, b = 2000 and c = 6000"
a + b = c
Multiply both sides by a + b
=> (a + b) (a + b) = c (a + b)
=> a*a + ab + ba + b*b = ca + cb
=> a*a + ab - ca = cb - b*b - ba
=> a( a + b -c) = -b(b + a - c)
so a = -b
=> a + b = 0

Can some one pls chk if the solved problem is wrong or intimate me where i have made a mistake

Answer 1

you cancelled a+b-c on the second to the last step....
the value of that is 0.

You cannot cancel with zero, as much as you cant divide by 0.©

Answer 2

I borrowed $4000 and after few days I again borrowed $2000 .When the other person asked me for the money
Question Details: I said
,
" the sum of 4000 and 2000 is equal to zero, so I do
not have
any balance to pay".

and i explained it with the algebric formulae " let a = 4000, b = 2000 and c = 6000"
a + b = c
Multiply both sides by a + b
=> (a + b) (a + b) = c (a + b)
=> a*a + ab + ba + b*b = ca + cb
=> a*a + ab - ca = cb - b*b - ba
=> a( a + b -c) = -b(b + a - c)

HERE IS YOUR ERROR. a+b-c=0… the next step you essentially factor out and multiply by the reciprocal of 0. 0 has no reciprocal. The rule is…
a=b => ac=bc. ac=bc => a=b IFF c≠0

so a = -b
=> a + b = 0

Can some one pls chk if the solved problem is wrong or intimate me where i have made a mistake

Answer 3

No, the following is not a valid mathematical step:
=> a( a + b -c) = -b(b + a - c)
so a = -b

to see notice that under your assumptions, a+b-c=0. Therefore, a and b could be anything and the first equation would still hold (say, a=1, b=2). Further, it is also easy to see you've made a mistake since you arrive at a result that must be false. Note that you've assumed that c=6000, and that a+b=c=6000, but then concluded that a+b=0 -- which is false under your assumptions!

Good luck!

Answer 4

The mistake here is factoring out (a+b-c), since a+b-c=0. You can't take out zero from both sides of an equation. You essentially did something like:

5 * 0 = 4 * 0
take out 0, you get

5=4

Answer 5

Please be honest even if others do not and even if others will not. Surely you don't have to give them that terrible reasoning. Return what you borrowed and then you will maintain your dignity in the sight of all people especially your creditors who trusted you with the money and especially helped you in your time of need.

Sorry, but you've made the mistake. No matter what you did to the $6,000 you borrowed is out of the question. Whether or not it is still with you is not anymore important. You have an obligation to pay them what you owe.

Answer 6

4th line down where you have:
a( a + b -c) = -b(b + a - c)

(a+b-c)= (4000+2000-6000) = 0
ditto for
(b+a-c)= (2000+4000-6000) = 0
you are multiplying by 0 and you get 0 = 0 while true in no way gets you out of debt.-sorry

Answer 7

a( a + b -c) = -b(b + a - c)

so a = -b

last step is wrong, you can not divide away the factor
(b + a - c)

because it equals zero.

you should say

a( a + b -c) = -b(b + a - c)

so a = -b , and (b + a - c) not zero
or (b + a - c) = 0

Answer 8

you can't cancel out (a+b-c) as the expression is equal to 0

Answer 9

The term (a+b-c) is zero. You can't divide this by zero; so what follows is incorrect.

Answer 10

=> a( a + b -c) = -b(b + a - c)
so a = -b

What happened to the ( a + b -c) and the (b + a - c) ?

Did you divide both sides? shame shame. you just divided by zero.