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 Problem: (x^2+1/x^2)-8(x-1/x)+14=0 [ Calculator, Method and examples ]Solution:Your problem -> (x^2+1/x^2)-8(x-1/x)+14=01(x^2+1/x^2)-8(x-1/x)+14=0Let x-1/x=m=>(x-1/x)^2=m^2=>x^2+1/x^2-2=m^2=>x^2+1/x^2=m^2 + 2Substituting this values in the given equation, we get(m^2+2)-8m+14=0=>m^2-8m+16=0=>m^2-8m+16 = 0=>(m)^2 - 2(m)(4) + (4)^2 = 0=>(m-4)^2 = 0=>(m-4) = 0=>m = 4Now, x-1/x=4=>x^2-1=4x=>x^2-4x-1=0=>x^2-4x-1 = 0factor is not possible for equation x^2-4x-1=0Solution is possible using the method of perfect square.Comparing the given equation with the standard quadratic equation ax^2+bx+c=0,we get, a=1, b=-4, c=-1.:. Delta=b^2-4ac=(-4)^2-4 (1) (-1)=16+4=20:. sqrt(Delta)=sqrt(20)=2*sqrt(5)Now, alpha=(-b+sqrt(Delta))/(2a)=(-(-4)+2*sqrt(5))/(2*1)=(4+2*sqrt(5))/2=2+sqrt(5) and, beta=(-b-sqrt(Delta))/(2a)=(-(-4)-2*sqrt(5))/(2*1)=(4-2*sqrt(5))/2=2-sqrt(5)

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