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 2 years 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! :)
 2 years 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! :)

This Question is Closed

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.1actually you might want to substitute x  3 with a instead to avoid confusion

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.1but you're right anyway... except for the last part

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.1wait on second thought you're right

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.1and 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?

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.1a^2  4a + 3 is factorable

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

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.1yeah. that one isn't factorable

mazehaq
 2 years ago
Best ResponseYou've already chosen the best response.1so 3  4a + a^2 is a^2  4a + 3 ...right?

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

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.1they shouldn't be equal...

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.1how did you factor a^2  4a + 3?

mazehaq
 2 years ago
Best ResponseYou've already chosen the best response.1I 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

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

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.1right. that's better

mazehaq
 2 years ago
Best ResponseYou've already chosen the best response.1So how do I solve the end?

mazehaq
 2 years ago
Best ResponseYou've already chosen the best response.1(x3)^1/3 (x4)(x6) = 0

mazehaq
 2 years ago
Best ResponseYou've already chosen the best response.1don't I make each = to zero

mazehaq
 2 years ago
Best ResponseYou've already chosen the best response.1Like, 2 of my answers will be 4 & 6...

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.1now..just equate (x3)^1/3 to 0

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.1\[(x  3)^{\frac 13} = 0\]

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.1take the cube root of both sides..what happens?

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.1so there's your answer

mazehaq
 2 years ago
Best ResponseYou've already chosen the best response.1Okay, so answer is 3,4,6 :) thanks!
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