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# hard algebra...

0
119
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question is f(x)= (2x^3/2 -3x^-3/2 )-5

and x>0

Sep 16, 2018

#1
+95282
+1

Are you sure that wasn't a +5 on the end?

$$f(x)=(2x^{3/2} -3x^{-3/2} )^2 -5\\ Find \;\;x\;\;when\;\;f(x)=5\\ (2x^{3/2} -3x^{-3/2} )^2 -5=5\\ (2x^{3/2} -3x^{-3/2} )^2 =10\\ 4x^3+9x^{-3}-12x^{0}=100\\ 4x^3+9x^{-3}-12x=100\\ 4x^6+9-12x^4=100x^3\\ 4x^6-12x^4-100x^3+9=0\\$$

Sep 16, 2018
#2
+1

Sorry there was a +5

Guest Sep 16, 2018
#3
+95282
+1

$$f(x)=(2x^{3/2} -3x^{-3/2} )^2 +5\\ Find \;\;x\;\;when\;\;f(x)=5\\ (2x^{3/2} -3x^{-3/2} )^2 +5=5\\ (2x^{3/2} -3x^{-3/2} )^2 =0\\ 4x^3+9x^{-3}-12x^{0}=0\\ 4x^3+9x^{-3}-12=0\\ 4x^6+9-12x^3=0\\ 4x^6-12x^3+9=0\\ let\;\;m=x^3\\ 4m^2-12m+9=0\\ (2m-3)^2=0\\ m=\pm\left[{\frac{3}{2}}\right]^{0.5}\\ x^3=\pm\left[{\frac{3}{2}}\right]\\ \text{But x is positive so}\\ x^3=\left[{\frac{3}{2}}\right]\\ x=\left[{\frac{3}{2}}\right]^{1/3}\\$$

1.5^(1/3) = 1.1447142425533319

x= 1.14   (to 3 significant figures)

That it the first bit, the second bit does not look too difficult, give it a try yourself.  :)

Sep 16, 2018
#4
+1

Thank you so much... I've given it a go and think I understand it now!!

Guest Sep 16, 2018
#5
+95282
0

That is excellent :)

Melody  Sep 17, 2018