anonymous
  • anonymous
i need help solving this: x^(2/3)-2x^(1/3)=15. And the intrsutions say explain and demonstrate how to use substitution to solve the equation. well i don't understand this at all. please help!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
treat x^(2/3) as x^(1/3)^2
anonymous
  • anonymous
ok put \[z=x^{\frac{1}{3}}\]
anonymous
  • anonymous
then factor as x^2-2x-15=0, and substitute x^1/3 back in for x

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anonymous
  • anonymous
then by the laws of exponents \[z^2=(x^{\frac{1}{3}})^2=x^{\frac{2}{3}}\]
anonymous
  • anonymous
so by replacing \[x^{\frac{1}{3}}\] by \[z\] you get an equation that looks like \[z^2-2z=15\]
anonymous
  • anonymous
so the answer should be 5?
anonymous
  • anonymous
there are two answers
anonymous
  • anonymous
and you can solve this for z by writing \[z^2-2z-15=0\] \[(z-5)(z+3)=0\] so \[z=5\] or \[z=-3\]
anonymous
  • anonymous
that is what i was getting 5 or -3 but then when i try to substitute back in i do not get anything that looks right. i absolutely think that i am doing something wrong still
anonymous
  • anonymous
but now we have to remember that \[z=x^{\frac{1}{3}}\]so that means that \[x^{\frac{1}{3}}=5\] or \[x^{\frac{1}{3}}=-3\]
anonymous
  • anonymous
and so \[x=(5)^2=125\] or \[x=(-3)^3=-27\]
anonymous
  • anonymous
so i substitute back in -25 or 127?
anonymous
  • anonymous
i mean -27 or 125
anonymous
  • anonymous
you substitute x^(1/3) back in for z
anonymous
  • anonymous
x^(1/3)=5 x^(1/3)=-3
anonymous
  • anonymous
then cube both sides of each equation to find x
anonymous
  • anonymous
(x^(1/3))^3=5^3 x=125 (x^(1/3))^3=-3^3 x=-27
anonymous
  • anonymous
so both are good solutions? im trying to follow sorry, i am just very bad at this
anonymous
  • anonymous
so both are good solutions? im trying to follow sorry, i am just very bad at this
anonymous
  • anonymous
Yes both are good solutions because they are in the domain of the original function.

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