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Math Challenge II-B Algebra 5.28

 
 
ShiJames的头像
Math Challenge II-B Algebra 5.28
ShiJames - 2020年07月16日 Thursday 11:44
 

After thinking about the problem for a while, I still do not know what to do for 5.28. I feel like it has something to do with the difference of cubes since x^3 and 8 are both cubes. Are there any strategies that I could try? Thank you.

 
ProfessorAreteem的头像
Re: Math Challenge II-B Algebra 5.28
ProfessorAreteem - 2020年07月16日 Thursday 13:01
 

Here you can "reduce the exponents" of the target expression. Since we know $x^3 + 4x = 8$, we have that $x^3 = 8 - 4x$. You can then use this to rewrite some portions of the target expression. Note that $x^7 = x^3 \cdot x^3 \cdot x$.

 
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