anonymous
  • anonymous
i need to solve the equation x^3=9x. it looks like it's supposed to be simple? but im lost...
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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welshfella
  • welshfella
write it as x^3 - 9x = 0 now can you factor the left side?
welshfella
  • welshfella
what is common to x^3 and 9x?
welshfella
  • welshfella
x right? so we have x(x^2 - 9) = 0 can you continue/

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welshfella
  • welshfella
if we have 2 functions multiplied together to give 0 then either of them will be 0
anonymous
  • anonymous
Im not sure how to continue from this point.. x(x^2-9)=0 but then what? I'm not sure how the final answer is supposed to look
tkhunny
  • tkhunny
Why did you stop factoring? Go!!
welshfella
  • welshfella
x^2 - 9
welshfella
  • welshfella
- do you recall the difference of 2 squares?
anonymous
  • anonymous
wait... where did you get x6-9 from i feel like im missing something significant here
welshfella
  • welshfella
- that was a typo! i meant x^2 - 9
anonymous
  • anonymous
oh okay phew-- so wait where we are now.. argh... I'm sorry I'm still confused... I don't know what i can factor out ?
welshfella
  • welshfella
x^2 - 9 is a difference of 2 squares x^2 is a perfect square and so is 9
welshfella
  • welshfella
so square root of x^2 is x and square root of 9 is 3 so we write these into 2 parentheses and + sign goes into one parenthese and - sign in the other x^2 - 9 = (x + 3)(x - 3)
welshfella
  • welshfella
so now we have x(x^2 - 9) = 0 x(x + 3)(x - 3) = 0
welshfella
  • welshfella
this means x and x + 3 and x- 3 can all be 0
anonymous
  • anonymous
so... okay that makes a bit more sense now.. so would that be the final answer?
welshfella
  • welshfella
no we need to find the values of x by solving 3 simple equations x = 0 - that's one root x + 3 = 0 and x - 3 = 0
welshfella
  • welshfella
x + 3 = 0 so x = ?
anonymous
  • anonymous
x would equal 3 and -3 right?
welshfella
  • welshfella
yes and dont forget the x = 0 Its a cubic equation ( as it hace x^3 in it) so there will be 3 solutions the solution set is {0, -3 , 3}
anonymous
  • anonymous
okay, i think I have a bit more of a grip on it now. Thank you so much for your help, I appreciate it a lot
welshfella
  • welshfella
yw

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