anonymous
  • anonymous
need help finding 2 solutions for this equation.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
\[y ^{2\over3}+5y ^{1\over3}-104=0\]
dumbcow
  • dumbcow
treat it just like a quadratic equation since (y^1/3)^2 = y^2/3 factor , what factors of -104 add up to 5
anonymous
  • anonymous
i couldn't think of anything that does.

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dumbcow
  • dumbcow
start with the obvious 52*2 then take half of 52 and double 2 26*4 13*8
anonymous
  • anonymous
-13 and 8 work I guess
dumbcow
  • dumbcow
check the signs, they need to add up to positive 5
anonymous
  • anonymous
13 and -8
dumbcow
  • dumbcow
ok so now (y^1/3 +13)(y^1/3 - 8) = 0 solve each part for y
anonymous
  • anonymous
so 13- 1/3 and 8-1/3? Sorry, I know this is way more simple than I'm making it.
anonymous
  • anonymous
i just don't know if it will end up not being a whole number this way? and what that would be exactly
dumbcow
  • dumbcow
thats ok y^1/3 = -13 to get y by itself i have to take each side to the 3rd power this way (y^1/3)^3 = y y = -13^3 also y = 8^3
anonymous
  • anonymous
oh ok. so the answers can be to the third power like that?
anonymous
  • anonymous
my online assignment wont let me type the answer to the third power. Do I solve more from there?
dumbcow
  • dumbcow
put it in your calculator to get a whole number
anonymous
  • anonymous
one of them is 28561 and the other is4096..? kinda big numbers.
dumbcow
  • dumbcow
8^3 = 8*8*8 = 512 -13^3 = -13*-13*-13 = -2197
anonymous
  • anonymous
ohho k, i didn't know the answers could be that large.
dumbcow
  • dumbcow
only because of the fractions in the exponents

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