I need to solve this and find exactly 2 solutions for a

[gloomy sedge]

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[acoustic aurora]

For the bottom one simplify for y in terms of x then substitute it into the first equation.

[grim wadi]

That doesn't work. Two equations, three variables. I'm thinking we don't have the full question.

[grim wadi]

What's the full question?

[earnest badge]

it's the full question

I can give you the right answer, but I don't know how to get it

[grim wadi]

I don't think it is.

[earnest badge]

it's not your typical algebra

[grim wadi]

I suspect that it's not algebra at all.

[earnest badge]

yes it is

[deep perch]

damn that looks hard

[grim wadi]

So you're telling me there's nothing to the left, to the right, above, or below the frame of the image you sent that has anything whatsoever to do with the question?

[grim wadi]

It looks impossible is how it looks.

[earnest badge]

(-inf, -6/5) u (-6/5, -1/6] u {0} u [1/6, 6/5) u (6/5, inf)

here's the correct answer

it's a parametric equation

[grim wadi]

...no it's very much not?

[earnest badge]

yes it is

[deep perch]

we clearly have y=+-ax

[arctic bolt]

mane wtf

[earnest badge]

how?

[grim wadi]

That's wrong.

[deep perch]

for what

[earnest badge]

for a

[deep perch]

what variable is this for?

okay

[grim wadi]

Not from the image you sent it's not.

[deep perch]

that isn't exactly 2 solutions

@earnest badge read the question clearly first and send us the full question

[earnest badge]

it's more like 2 roots

find all solutions for a with 2 roots

[deep perch]

just send the full problem

bro

[earnest badge]

it's the full problem

[deep perch]

did they provide you with that exact picture?

[grim wadi]

You said that before and you were wrong.

[earnest badge]

yes

[earnest badge]

how am I wrong

[deep perch]

change schools

good luck with your life ahead

rooting for you

[earnest badge]

it's will be on my final exam

[grim wadi]

Because what you're saying now is different from what you were saying before.

[earnest badge]

what did I say before?

[grim wadi]

And you said what you were saying before was the full question.

Just send us a picture of the original text of the question.

We need to know what the question says, not what you think the question says.

[acoustic aurora]

How are we supposed to find exactly two equations for "a"?

Sounds contradicting.

[earnest badge]

Find all values ​​of "a", for each of which the system of equations has exactly two different solutions

this is exactly what the problem is saying

[earnest badge]

.

[earnest badge]

.

and this is the correct answer to this problem: (-inf, -6/5) u (-6/5, -1/6] u {0} u [1/6, 6/5) u (6/5, inf)

but I don't know how to get it

[grim wadi]

That's literally the third time you've said that. I have no reason to believe you. Why will you not just take a picture of the goddamn text of the goddamn question?

[tulip trail]

hahaha wow

I think what he means is that we have to find all possible $a\in\bR$ such that there exist 2 distinct pairs $(x,y)\in\bR^2$ which solve this idiotic system of equations

[shut talon]

No Lifer #GTFOanemia

[tulip trail]

$4-y^2 = 4-a^2x^2$

[shut talon]

No Lifer #GTFOanemia

[tulip trail]

$y^2=a^2x^2$

[shut talon]

No Lifer #GTFOanemia

[tulip trail]

$y=\pm ax$

$x^2+5a^2x^2 = 12x\pm10ax$

[shut talon]

No Lifer #GTFOanemia

No Lifer #GTFOanemia

[tulip trail]

$x^2(1+5a^2)-x(12\pm10)=0$

$x(1+5a^2)-12\mp10=0$

[shut talon]

No Lifer #GTFOanemia

[tulip trail]

$x = \frac{22}{1+5a^2},\frac2{1+5a^2}$

[shut talon]

No Lifer #GTFOanemia

[tulip trail]

$y = \frac{484a^2}{25a^4+10a^2+1},\frac{4a^2}{25a^4+10a^2+1}$

[shut talon]

No Lifer #GTFOanemia

[tulip trail]

what

[deep perch]

yapperz

[tulip trail]

yeah question weird

[tulip trail]

anyways coffey I need help in real analysis (help-uni)

[earnest badge]

can you explain the solution please

[grim wadi]

I don't care what he means, I care what the question is.

[earnest badge]

It's the question, I put it in Google Translate for you

[deep perch]

is English not your first language

[earnest badge]

No

[deep perch]

f

[tulip trail]

brrrr I need to understand the goddamn question for that-

[tulip trail]

oh well

[earnest badge]

"Find all values ​​of "a", for each of which the system of equations has exactly two different solutions"

this is the literal translation of the question, there's nothing more or less

"(-inf, -6/5) u (-6/5, -1/6] u {0} u [1/6, 6/5) u (6/5, inf)"

this is the correct answer for the problem

[earnest badge]

.

[earnest badge]

It's upsetting that you would assume I'm hiding the original problem from you. I provided you with the original text and even discovered a similar problem with a solution.

[earnest badge]

@grim wadi @deep perch

[deep perch]

dude you clearly hid the question

you have to understand that we aren't obliged to help you, techie did it out of his own good will so you must cooperate!

[earnest badge]

how

the question is literally in the title, what difference will it make if I send the problem in my language? The google translate will give you the same result

[deep perch]

"I need to solve this and find exactly 2 solutions for a" and "Find all value of a, for each of which the system of equations has exactly two different solution"
ARE NOT THE SAME

[earnest badge]

I literally said it right here, find the values of a

[deep perch]

by that time techie had left

we thought you'd give us wrong information again and we'd end up jabbing at an erroneous question

[earnest badge]

no, Techie responded with "That's the third time you've said it"

[deep perch]

he did

he left after that

[earnest badge]

I asked chat gpt if they're the same, "Yes, both statements are asking for the same thing – to find values of "a" for which a system of equations has exactly two different solutions."

[acoustic aurora]

ChatGPT is one of the most trash things humans created for math related things.

If you say "is 1 + 1 = 3" it will say yes.

[tulip trail]

ok it's not that idiotic lol but for proper problems it just dies

[deep perch]

it is that idotic

it literally cant count bro

it literally cant even replace "." in a text with "->"s

[tulip trail]

wait what

wow

[graceful salmon]

its not, one means that we need to find 'exactly two value of a"
while the question really means find 'all the value of a' for which the system of eq has exactly 2 solutions
in first one 'a' is a varaible while in second one 'a' is a coeffeicnent

i think we can proceed this question
firstly find the domain of the y = +- ax due to the log fucntion

then if we see the graph of the ellipse in second equation

it passes through origin thefore the a for which it is tangent at the point that will be excluded

ig thats why + - 6/5 is excluded

and rest is excluded due to domain ig

if i am wrong please someone do correct me cz i am not 100% sure

[tulip trail]

um the solution already got posted lol

[graceful salmon]

wait it did?

[tulip trail]

this

[graceful salmon]

oh lol i didnt see lol

[tulip trail]

yeah

uh hi? if you want to talk regularly general chat is there

[surreal trench]

No

Please help

[tulip trail]

ok then make a help post

[surreal trench]

https://discord.com/channels/624314920158232616/1231189315904606208

[tulip trail]

I can't help you in an existing help thread

[tulip trail]

ok yeah I've seen this reel lol
some dude gaslighted chatgpt