Question

If x-1/x =3/2 then find x+1/x and x⁴+1/x⁴

Answer 1

Answer:

x-1/x=3/2

(x-1/x)^2=(3/2)^2

=> x^2+1/x^2-2.x.1/x=9/4

=> x^2+1/x^2-2=9/4

=> x^2+1/x^2=9/4+2=(9+8)/4=17/4

=> (x^2+1/x^2)^2=(17/4)^2

=> x^4+1/x^4+2.x^2.1/x^2=289/16

=> x^4+1/x^4+2=289/16

=> x^4+1/x^4=289/16-2

=> x^4+1/x^4=(289-32)/16=257/16

so, x^4+1/x^4=257/16