Question

Solve for x: 4(x-1/x)^2+ 8(x +1/x)=29​

Answer 1

Answer:

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Answer 2

Answer:

(x-1/x)^2+8(x+1/x)=29

Put (x-1/x)^2=(x+1/x)^2–4

or (x+1/x)^2–4+8(x+1/x)-29=0

Let (x+1/x)=p

or p^2+8p-33=0

or p^2+11p-3p-33=0

or p(p+11)-3(p+11)=0

or (p+11)(p-3)=0

p=-11 , 3

Put p=-11

x+1/x=-11

or x^2+1=-11x

or x^2+11x+1=0

or x^2+2×x×11/2+(11/2)^2=121/4–1

or (x+11/2)^2=117/4

or x+11/2=+/-(1/2).(117)^1/2

or x=[-11+/-(117)^1/2] /2 , Answer

Now put p=3

x+1/x=3

or x^2+1=3x

or x^2–3x+1=0

or (x)^2–2×x×3/2+(3/2)^2=9/4–1

or (x-3/2)^2=5/4

or x-3/2=+/-(1/2).(5)^1/2

or x=[3+/-(5)^1/2]/2 , Answer