Given that, x2-3=22 =x2=3+22 =x2=2+22+1 =x2=(2)2+2×2×1+11 =x2=(2+1)2=x=2+1 Now, x=2+1 =1x=2-1(2+1) (2-1) =1x=2-1(2)2-12 =1x=2-12-1 =1x=2-11 ∴1x=2-1
Now, x4+1x4 =(x2)2+(1x2)2 =(x2+1x2)2-2×x2×1x2 =(x2+1x2)2-2 ={(x+1x)2-2×x×1x}2-2 ={(x+1x)2-2}2-2 ={(2+1+2+1)2-2}2-2 ={22)2-2}2-2 =(4×2-2)2-2 =(8-2)2-2 =62-2 =36-2 =34
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