Hello. Can someone help me solve this. If x+y=8, xy+1/xy=22, then what is y+1/x? | Mathematics | Page 1

mighty estuaryBOT Mar 4, 2024, 7:15 AM

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mint finch Mar 4, 2024, 7:20 AM

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8-x/x I guess

cobalt spoke Mar 4, 2024, 7:23 AM

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mint finch 8-x/x I guess

why?

mint finch Mar 4, 2024, 7:29 AM

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cus if you rearrange the first equation it becomes y=8-x

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then you substitute that in y+1/x

cobalt spoke Mar 4, 2024, 7:30 AM

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dont u need to use the other equation?

mint finch Mar 4, 2024, 7:32 AM

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true

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did they give you an answer sheet

cobalt spoke Mar 4, 2024, 7:32 AM

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no just questions

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can i use the 2nd equation to get 1/x?

mint finch Mar 4, 2024, 7:34 AM

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I think it’s possible

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you just have to rearrange the equation to make the letter you want the subject

cobalt spoke Mar 4, 2024, 7:36 AM

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yeah thanks

mint finch Mar 4, 2024, 7:37 AM

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np if it doesn’t work let me know

primal kite Mar 4, 2024, 7:43 AM

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cobalt spoke yeah thanks

you can find x in terms of y for both equations ( or vice versa ), equate the 2 and solve

cobalt spoke Mar 4, 2024, 7:52 AM

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yeah. but i end up having a hard time

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i cant solve it

primal kite Mar 4, 2024, 7:53 AM

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show me your work

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@cobalt spoke

cobalt spoke Mar 4, 2024, 7:56 AM

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wait

mint finch Mar 4, 2024, 8:00 AM

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cobalt spoke yeah. but i end up having a hard time

what did you do?

cobalt spoke Mar 4, 2024, 8:04 AM

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like this

cobalt spoke Mar 4, 2024, 8:08 AM

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mint finch what did you do?

here

primal kite Mar 4, 2024, 8:13 AM

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try substituting the first equation into the second

cobalt spoke Mar 4, 2024, 8:14 AM

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why?

primal kite Mar 4, 2024, 8:14 AM

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that is how you find a solution for 2 equations

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you find x in terms of y or vice versa for 1 and substitute it in the other

cobalt spoke Mar 4, 2024, 8:18 AM

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yeah but i still can not get its numerical value

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i already tried it

mint finch Mar 4, 2024, 8:19 AM

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its better to make y the subject right?

cobalt spoke Mar 4, 2024, 8:20 AM

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i ended up getting y=8xy^2-22xy-1/xy^2

cobalt spoke Mar 4, 2024, 8:20 AM

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mint finch its better to make y the subject right?

what do you mean?

mint finch Mar 4, 2024, 8:20 AM

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cobalt spoke what do you mean?

make the equation to y= 8-x

cobalt spoke Mar 4, 2024, 8:21 AM

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already did

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mint finch Mar 4, 2024, 8:21 AM

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then you can substitute the y= 8-x in the second equation and replace the y with 8-x

cobalt spoke Mar 4, 2024, 8:22 AM

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no i cant

mint finch Mar 4, 2024, 8:22 AM

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cobalt spoke no i cant

why

cobalt spoke Mar 4, 2024, 8:22 AM

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im stuck

primal kite Mar 4, 2024, 8:22 AM

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cobalt spoke yeah but i still can not get its numerical value

you can factorise the cubic

cobalt spoke Mar 4, 2024, 8:23 AM

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primal kite you can factorise the cubic

but its not cubic

primal kite Mar 4, 2024, 8:24 AM

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cobalt spoke but its not cubic

sorry i meant quartic

cobalt spoke Mar 4, 2024, 8:24 AM

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i ended up getting y=8xy^2-22xy-1/xy^2

primal kite Mar 4, 2024, 8:24 AM

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lemme see if i cna reduce it to a lower degree eq

primal kite Mar 4, 2024, 8:24 AM

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cobalt spoke

divide both sides by y it becomes cubic

cobalt spoke Mar 4, 2024, 8:24 AM

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i dunno how

primal kite Mar 4, 2024, 8:24 AM

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cobalt spoke i dunno how

... divide by y ?

cobalt spoke Mar 4, 2024, 8:25 AM

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but it has 1?

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so i will still end up 1/y?

primal kite Mar 4, 2024, 8:31 AM

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hey i tried solving

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i got (4±(sqrt(27±sqrt(120)))

cobalt spoke Mar 4, 2024, 8:32 AM

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really? how?

primal kite Mar 4, 2024, 8:40 AM

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hold on let me write it down properly

cobalt spoke Mar 4, 2024, 8:41 AM

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ok

mint finch Mar 4, 2024, 9:17 AM

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so how’s the progress

primal kite Mar 4, 2024, 9:19 AM

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i think theres no real soltutons

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wait. theres 2

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x+y=8
xy+1/xy=22

let xy=t

t+1/t=22

t^2-22t+1=0

(t-11)^2=120

t=11±sqrt120

x(8-x)=11±sqrt120

x^2-8x=-11±sqrt120

(x-4)^2=5±sqrt120

x=4±(sqrt(5±sqrt120))

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5-sqrt120 is negative so for real solutions, x=4±sqrt(5+sqrt120) @cobalt spoke

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@mint finch

mint finch Mar 4, 2024, 10:18 AM

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primal kite i think theres no real soltutons

really meh

primal kite Mar 4, 2024, 10:19 AM

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nvm theres 2

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real solutin

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and 2 complex

mint finch Mar 4, 2024, 10:19 AM

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if there’s no real solutions then why would they give that question

mint finch Mar 4, 2024, 10:19 AM

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primal kite nvm theres 2

oh ok

primal kite Mar 4, 2024, 10:19 AM

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mint finch if there’s no real solutions then why would they give that question

yeeh

#Hello. Can someone help me solve this. If x+y=8, xy+1/xy=22, then what is y+1/x?