Question

if x=2+root 3,find( i) x²+1/x² (ii) x⁴+1/x⁴
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Answer 1

Step-by-step explanation:

x=2+√3

1/x=2-√3........ on rationalisation

x+1/x=2+√3+2-√3

x+1/x=4

(x+1/x)²=4²

x²+1/x²+2(x)(1/x)=16

x²+1/x²+2=16

x²+1/x²=14

x²+1/x²=14

(x²+1/x²)²=14²

x⁴+1/x⁴+2(x²)(1/x²)=196

x⁴+1/x⁴+2=196

x⁴+1/x⁴=194