Question

solve the equation (x+1/x)^2=2(x+1/x)+3​

Answer 1

Answer:

hence x=1,1,(1±√-3)/2

Step-by-step explanation:

(x+1/x)^2=2(x+1/x)+3​

LET x+1/x=y

y²=2y+3

y²-2y-3=0

y²-3y+y-3=0

y(y-3)+(y-3)=0

(y-3)(y+1)=0

y=3 OR -1

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So

1+x+1/x=3

x+x2+1=3x

x2-2x+1=

(x-1)²=0

so x=1,1

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also

x+1/x=-1

x2+1=-x

x2-x+1=0

x=( 1±√1-4)/2

=(1±√-3)/2

hence x=1,1,(1±√-3)/2