Question

if x=3+2√2 then find the value of x²+1/x²

please help in this

Answer 1

Hey friend

Here is your answer

x=3+2√2

1/x=1/(3+2√2)

Rationalising denominator

1/x=(3-2√2) / [(3+2√2)(3-2√2)]

[USING (a+b)(a-b) =a²-b²]

1/x=(3-2√2) / [(3)²-(2√2)²]

1/x=(3-2√2) / (9-8)

1/x=3-2√2

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=x²+1/x²

=(3+2√2)²+(3-2√2)²

=(3)²+(2√2)²+2×3×2√2+(3)²+(2√2)²-2×3×2√2

=9+8+12√2+9+8-12√2

=9+8+9+8

=34

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HOPE THIS HELPS YOU

Answer 2

1/x= 1/3+2√2
1/x= 3-2√2/1. (Rationalize the term)
x+1/x= 3+2√2+3-2√2
x+1/x= 6
(x+1/x)2= (6)2. (Squaring the both sides)
x2+1/x2+2×x×1/x= 36
x2+1/x2+2= 36
x2+1/x2= 34.