Solve x^2+ 4/(x^2)=12 for all real values of x
Please show me how to solve this without a calculator!
Original post by Phoenix Everill
Please show me how to solve this without a calculator!
Multiply both sides by and solve. Please post your working if you need any further hints.
Original post by RogerOxon
Multiply both sides by and solve. Please post your working if you need any further hints.
Original post by Phoenix Everill
Please show me how to solve this without a calculator!
just put the second term into terms of x^(-2), using the 4.
then solve
Original post by ThatsAGoodOne349
just put the second term into terms of x^(-2), using the 4.
then solve
then solve
Thank you for your reply
so:
x^4 + 4 = 12x^2
=> x^4 + 4 - 12 = 0
=> x^2 + 4x^(-2) -12 = 0
Then I don't know how to solve, sorry.
Original post by Phoenix Everill
Thank you for your reply
so:
x^4 + 4 = 12x^2
=> x^4 + 4 - 12 = 0
=> x^2 + 4x^(-2) -12 = 0
Then I don't know how to solve, sorry.
so:
x^4 + 4 = 12x^2
=> x^4 + 4 - 12 = 0
=> x^2 + 4x^(-2) -12 = 0
Then I don't know how to solve, sorry.
you got that right
Google time
Original post by Phoenix Everill
Thank you for your reply
so:
x^4 + 4 = 12x^2
=> x^4 + 4 - 12 = 0
=> x^2 + 4x^(-2) -12 = 0
Then I don't know how to solve, sorry.
so:
x^4 + 4 = 12x^2
=> x^4 + 4 - 12 = 0
=> x^2 + 4x^(-2) -12 = 0
Then I don't know how to solve, sorry.
(we need to ignore x=0, if it were a solution)
Now solve it as a quadratic in .
Original post by Phoenix Everill
Thank you for your reply
so:
x^4 + 4 = 12x^2
=> x^4 + 4 - 12 = 0
=> x^2 + 4x^(-2) -12 = 0
Then I don't know how to solve, sorry.
so:
x^4 + 4 = 12x^2
=> x^4 + 4 - 12 = 0
=> x^2 + 4x^(-2) -12 = 0
Then I don't know how to solve, sorry.
Original post by ThatsAGoodOne349
you got that right
Nope - the intermediate step is wrong. What happened to the in the second line?
Original post by RogerOxon
Nope. What happened to the ?
nono
you got rid of the fraction
try using the x^4 +4 = 12x^2 and using this:
y =x^2
Original post by Phoenix Everill
Thank you for your reply
so:
x^4 + 4 = 12x^2
=> x^4 + 4 - 12 = 0
=> x^2 + 4x^(-2) -12 = 0
Then I don't know how to solve, sorry.
so:
x^4 + 4 = 12x^2
=> x^4 + 4 - 12 = 0
=> x^2 + 4x^(-2) -12 = 0
Then I don't know how to solve, sorry.
Original post by ThatsAGoodOne349
you got that right
Google time
Google time
They didn't - the bold line is wrong.
Original post by RogerOxon
(we need to ignore x=0, if it were a solution)
Now solve it as a quadratic in .
(we need to ignore x=0, if it were a solution)
Now solve it as a quadratic in .
Original post by ThatsAGoodOne349
nono
you got rid of the fraction
you got rid of the fraction
Why do you think that's a problem?
Original post by RogerOxon
Why do you think that's a problem?
My last post...
Original post by ThatsAGoodOne349
My last post...
You must have misread what I posted. We're in violent agreement.
Original post by RogerOxon
You must have misread what I posted. We're in violent agreement.
LOL
okay
let's go with the substitution thing
@RogerOxon
you didn't mention substitution inn that post
you didn't mention substitution inn that post
Original post by ThatsAGoodOne349
@RogerOxon
you didn't mention substitution inn that post
you didn't mention substitution inn that post
What substitution?
Original post by RogerOxon
What substitution?
y=x^2
Quick Reply
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