How to know the no. of possible values

[hoary snow]

can we know that only by manuplating the expression. Like in this one question we could see two possible values of r by manipulating the expression.

But sometimes we may miss one particular value, that exists. Any other aspect to this

[fallow basin]

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[orchid egret]

İf all of them gets the same value they will be equal if this has anothor solution only god knows about it

[opaque charm]

assume a>b and compare (b+c+d)/a and (a+c+d)/b

sorry for late reply; i somehow forgot this existed

[hoary snow]

its 3 and -1

[hoary snow]

oh its okay

[hoary snow]

what do we gain from doing this

[opaque charm]

because they’re meant to be equal

hint: they aren’t equal

[hoary snow]

well I am not getting it

[opaque charm]

if a>b
(b+c+d)/a < (a+c+d)/a < (a+c+d)/b

[rocky garden]

wait it doesn’t say that a,b,c,d are distinct

[opaque charm]

correct!

because if any two variables are distinct, then the equation does not hold true!

[rocky garden]

oh shit

[opaque charm]

there’s actually a far easier way to do this if you add 1 to everything in the equation

[rocky garden]

yeah ik

but still

[opaque charm]

(a+b+c+d)/a = (a+b+c+d)/b = … = r+1

[rocky garden]

fear is now instilled within me

[opaque charm]

you get a=b=c=d almost instantly

[opaque charm]

why?

[rocky garden]

the pure fact that this problem is crumbled by non-distinct variables

has now instilled a new mathematical fear in me

[opaque charm]

ok

[rocky garden]

so a=b=c=d=r+1

wait i know the solution now 💀

[opaque charm]

no

[rocky garden]

oh wait i am stupid

[opaque charm]

a=b=c=d, so (a+b+c)/d = 3a/a = 3

[rocky garden]

HEHEHEHA

[hoary snow]

thanks @opaque charm @rocky garden @orchid egret

[modern oriole]

@hoary snow has given 1 rep to @rocky garden @umbral stirrup @orchid egret

[hoary snow]

+close