Question

:if x=7+4√3find the value of (x-1/x)^3

Answer 1

Sol:
Given  x = 7 + 4√3   

x = 7 + 4√3

1 / x = 1 / ( 7 + 4√3)  rationalize denominator (7 - 4√3)

= (7 - 4√3) / 49 - 48 = (7 - 4√3)

1) x + 1 / x = 7 + 4√3 + 7 - 4√3 = 14.

And √x = √( 7 + 4√3 ) = √ ( √4)2 + (√3)2 + 2x√4x√3 )

√x = √4) + (√3) = 2 + √3 .

⇒ 1 / √x  = 1 / ( 2 + √3 )  rationalize denominator (2 - √3) then

⇒ 1 / √x  = 2 - √3

2) √x +1 / √x = 2 + √3 + 2 - √3 = 4