Q)IF X- 1/X=3 + 2 ROOT 2, THEN FIND THE VALUE OF X3 - 1/X3 .
Question : to find the value of x3-1/x3
Given : x - 1/x = 3+ 2√2
Squaring both sides:
(x-1/x)2= (3+ 2√2)2
x2+ 1/x2-2=9+8+ 12√2
x2 + 1/x2 = 19+ 12√2
Answer: by using identity a3-b3 = (a-b)(a2+b2+ab)
(x)3 - (1/x)3 = (x-1/x)(x2+1/x2+1)
= (3+ 2√2)(19+12√2+1)
= (3+2√2)(20+12√2)
= (60+36√2+40√2+48)
= 108+76√2
= 108+107.464
= 215.464 - Answer
Hit THumbs up if you like my answer
Answer: