x=3+2√2
Find: x⁴+1/x⁴
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x = 3 +2√2
1/x = 3 - 2√2
So, x +1/x = 3 + 2√2 +3 -2√2 = 6
So, x² + 1/x² = (x +1/x)² -2x.1/x
= ( 6)² -2 = 34
again,
x⁴ + 1/x⁴ = ( x² +1/x²)² -2x².1/x²
=(34)² -2 = 1156 -2 = 1154
1/x = 3 - 2√2
So, x +1/x = 3 + 2√2 +3 -2√2 = 6
So, x² + 1/x² = (x +1/x)² -2x.1/x
= ( 6)² -2 = 34
again,
x⁴ + 1/x⁴ = ( x² +1/x²)² -2x².1/x²
=(34)² -2 = 1156 -2 = 1154
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