Mathematics
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OpenStudy (anonymous):
x^2/5-x^1/5-2=0
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OpenStudy (anonymous):
i think this is my last one
OpenStudy (anonymous):
any help please
OpenStudy (anonymous):
im tired only 3 hours of sleep this morning
hero (hero):
Hint:
\[(x^{1/5})^2 - x^{1/5} - 2 = 0\]
OpenStudy (anonymous):
i hate fractions. But ill try x^1/10-x^1/5-2=0
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hero (hero):
No, that's not the next step. Think quadratically
OpenStudy (anonymous):
add 2 to the other side!
OpenStudy (anonymous):
or mx+b
hero (hero):
no
OpenStudy (anonymous):
hold on i think i got it!
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OpenStudy (anonymous):
u^2-x^5-2=0
OpenStudy (anonymous):
(x+2)(x-1)
OpenStudy (anonymous):
oh the (x-2)(x+1) then set them to 0 so x=2 x=-1
OpenStudy (anonymous):
right? (2,-1)
OpenStudy (klimenkov):
Yes. But now make the inverse substitution to get the solution!
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OpenStudy (anonymous):
I did. Didn't I?
OpenStudy (klimenkov):
What is the solution of your origin equation? Type it right here!
OpenStudy (anonymous):
2,-1?
OpenStudy (anonymous):
I need to go for a few mintutes
OpenStudy (anonymous):
but its all there
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OpenStudy (klimenkov):
If it is so, what will be \(\sqrt[5]{-1}\) ?
OpenStudy (anonymous):
-5
OpenStudy (anonymous):
Im lost!
hero (hero):
u = x^(1/5)
u^2 - u - 2 = 0
(u-2)(u + 1) =0
u - 2 = 0
u + 1 = 0
x^(1/5) - 2 = 0
x^(1/5) + 1 = 0
x^(1/5) = 2
x^(1/5)^5 = 2^5
x = 2^5
x = 32
x^(1/5)^5 = -1^5
x = -1
OpenStudy (anonymous):
oh thank you