Question

if x-1/x= 3 +2 square root 2 ... find the value of 1/4 (x^3-1/x^3)

Answer 1

x - 1/x = 3 +2√2

x³ -1/x³ =(x -1/x)³ +3(x -1/x)

=(3+2√2)³ +3(3+2√2)

=(3+2√2){17+12√2 + 3}

=( 3+2√2){20+12√2)

=4(3+2√2)(5+3√2)

=4(15 +9√2 +10√2+12)

=4(27 +19√2)

now, 1/4( x³ -1/x³) =1/4{4(27+19√2}

=(27+19√2) ( answer )