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3(x3)^1/3  4(x3)^4/3 + (x3)^7/3 = 0
To make it easier, I substituted (x3) with x, in which I got x^1/3(3  4x +x^2) ...but it can't be factored. Help me out! It's a fairly easy question I bet, but I need a nice way of solving it. Thank you! :)
 one year ago
 one year ago
3(x3)^1/3  4(x3)^4/3 + (x3)^7/3 = 0 To make it easier, I substituted (x3) with x, in which I got x^1/3(3  4x +x^2) ...but it can't be factored. Help me out! It's a fairly easy question I bet, but I need a nice way of solving it. Thank you! :)
 one year ago
 one year ago

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lgbasalloteBest ResponseYou've already chosen the best response.1
actually you might want to substitute x  3 with a instead to avoid confusion
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
but you're right anyway... except for the last part
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
wait on second thought you're right
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
and it can be factored... \[\huge a^{\frac 13} (3  4a + a^2) \implies a^{\frac 13} (a^2  4a + 3)\] can you see it now?
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
a^2  4a + 3 is factorable
 one year ago

mazehaqBest ResponseYou've already chosen the best response.1
Oh okay! I kept thinking that it was a^2 + 4a  3
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
yeah. that one isn't factorable
 one year ago

mazehaqBest ResponseYou've already chosen the best response.1
so 3  4a + a^2 is a^2  4a + 3 ...right?
 one year ago

mazehaqBest ResponseYou've already chosen the best response.1
So wait, how would I figure out the final answer, I am at (x3)^1/3 (x7)(x7)=0
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
they shouldn't be equal...
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
how did you factor a^2  4a + 3?
 one year ago

mazehaqBest ResponseYou've already chosen the best response.1
I skipped a few steps. Remember a = (x3) a^1/3 (a1)(a3) = 0 (x3)^1/3 [(x31)(x33)] = 0 (x3)^1/3 (x4)(x6) = 0
 one year ago

mazehaqBest ResponseYou've already chosen the best response.1
sorry about my previous comment tho, I totally typed it wrong, my computer is lagging so bad.
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
right. that's better
 one year ago

mazehaqBest ResponseYou've already chosen the best response.1
So how do I solve the end?
 one year ago

mazehaqBest ResponseYou've already chosen the best response.1
(x3)^1/3 (x4)(x6) = 0
 one year ago

mazehaqBest ResponseYou've already chosen the best response.1
don't I make each = to zero
 one year ago

mazehaqBest ResponseYou've already chosen the best response.1
Like, 2 of my answers will be 4 & 6...
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
now..just equate (x3)^1/3 to 0
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
\[(x  3)^{\frac 13} = 0\]
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
take the cube root of both sides..what happens?
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
so there's your answer
 one year ago

mazehaqBest ResponseYou've already chosen the best response.1
Okay, so answer is 3,4,6 :) thanks!
 one year ago
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