Question

if x=3+2√2 find the value of x²+1/x² and x⁴+1/x⁴​

Answer 1

Answer:

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Answer 2

Answer:

x²+1/x² = 18/17

x⁴+1/x⁴ = 146/145.

Step-by-step explanation:

Given,

x = 3+2√2

Now consider,

x²+1/x²

= (3+2√2)²+1/(3+2√2)²

= [9+(4×2)]+1/[9+(4×2)]

= 9+8+1/9+8

= 18/17

:. x²+1/x² = 18/17.

Now consider,

x⁴+1/x⁴

= (3+2√2)⁴+1/(3+2√2)⁴

= [81+(16×4)]+1/[81+(16×4)]

= 81+64+1/81+64

= 146/145

:. x⁴+1/x⁴ = 146/145.