Question 507728: by using an appropriate substitution find the value of x for which x^(3/2) - 8x^(-3/2) =7
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the value of x for which x^(3/2) - 8x^(-3/2) =7
x^(3/2) - 8x^(-3/2) =7
x^(3/2) - 8/x^(3/2) -7=0
let u=x^(3/2)
u-8/u-7=0
multiply both sides by u
u^2-8-7u=0
u^2-7u-8=0
(u-8)(u+1)=0
u=8
or
u=-1
..
solving for x
For u=8
8=x^(3/2)
raise both sides to 2/3 power
x=8^(2/3)=4
..
For u=-1
-1=x^(3/2)
raise both sides to 2/3 power
x=(-1)^(2/3)=1
..
Check:
x^(3/2) - 8/x^(3/2) -7=0
for x=4
8-1-7=0
Therefore, 4 is a valid root
..
for x=1
1-8-7≠0, therefore, 1 is an extraneous root probably because we used u, the variable, as the common denominator in solving for u as above.
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