Question #22214

Solve each quadratic in form equation.
7. 6x^(2/3)-5x^(1/3)-6=0
8. x^(-2)+4x^(-1)=12

Expert's answer

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

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

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