Question

If x(x-2)=1, then the x²-1/x² is ?

Answer 1

Step-by-step explanation:

x²-2x=1

or, x²-2x-1=0

or, x=(-b+√(b²-4ac))/2a,(-b-√(b²-4ac))/2a

or, x=(-(-2)+√((-2)²-4*1*(-1)))/2*1,(-(-2)-√((-2)²-4*1*(-1)))/2*1

or, x=(2+√(4+4))/2,(2-√(4+4))/2

or x=(2+2√2)/2,(2-2√2)/2

or, x=1+√2,1-√2

x²-1/x²=(1+√2)² - 1/(1+√2)²

=(1+√2)²-(1-√2)²/(1+√2)² (1-√2)²

=(1+√2)²-(1-√2)²/(1²-(√2)²)(1²-(√2)²)

=(1+√2)²-(1-√2)²/(1-2)(1-2)

=(1+√2)²-(1-√2)²/-1*-1

=(1+√2)²-(1-√2)²/1

=4*1*√2

=4√2

you will get another answer by putting the other value of x