SOLUTION: Hi, would you help me solve this problem, please? Directions: Solve the equation by making the appropriate substitution. (meaning "u" for "x"). {{{ x^(7/2)-6x^(7/4)+9=0 }}}

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Question 906528: Hi, would you help me solve this problem, please?
Directions: Solve the equation by making the appropriate substitution. (meaning "u" for "x").

I let and , but am unsure of how to take it from there.
**All of the numerators of the exponents are 7, just in case that got cut off in the formula plotting system.


Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
There is a way to make the plotting system handle fraction exponents,
Place the expression in a 2x1 matrix with the blank character "" as the
upper element and the fraction exponent as the lower element.

Don't let u=x. Let  and . You had that right. 



becomes



Then factor:



And there's just one solution, u=3

Then  becomes



Then we raise both sides to the 'reciprocal'th power, 
the ths power




When you multiply those exponents on the right you get


  



The answer is 'the seventh root of three to the fourth power'.
 
or approximately 1.873444005

Edwin

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