Question

if x=3-2√2, find the value of x²+1\x²

Answer 1

If x = 3-2*2½
x² = (3-2*2½)²
(3²)+(2*2½)-2*(3)(2*2½)
9+8-12*2½
17-12*2½
x² = 17-12*2½
1. 1
--- = ------------
x² 17-12*2½

After rationalizing,
1
----- = 17+2*2½
x²
x²+1
---- = 17-12*2½+17+12*2½
x²
34-12*2½+12*2½
34+0
= 34