Answer to Question #22214 in Algebra for Brenden Fields

Question

Solve each quadratic in form equation.

7. 6x^(2/3)-5x^(1/3)-6=0

8. x^(-2)+4x^(-1)=12

Answer 1

7. 6x^(2/3)-5x^(1/3)-6=0
let x^(1/3)=t then
6t^2-5t-6=0
D=25+4*6*6=25+144=169
t=(5+-sqrt(169))/12=(5+-13)/12
t1=3/2 or t2=-2/3
then x^(1/3)=3/2 or x^(1/3)=-2/3
SO x=27/8 or x=-8/27

8.x^(-2)+4x^(-1)=12 let x^(-1)=t thent^2+4t=12
t^2+4t+4=16
(t+2)^2=16
t+2=+-4
t=-2+-4
t=-6 or t=2
so x=-1/6 or x=1/2