If x = 3 + √8 find the value of x + 1 / x
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x = 3 + root8
x2 = 9 + 8 + 6root8
x2 = 17 + 6root8
1/x2 = 1/17 + 6root8
1/x2 = 17 - 6roo8/1 ( by rationalising the denominator we get this..)
1/x2 = 17 - 6root8
now,
x2 + 1/x2 = 17 + 6root8 + 17 - 6root8
x2 + 1/x2 = 34
then (x+1/x) square = x2 + 2 + 1/x square
(x+1/x) square = 34 + 2
(x+1/x) square = 36
then x+1/x = +6 or -6
x2 = 9 + 8 + 6root8
x2 = 17 + 6root8
1/x2 = 1/17 + 6root8
1/x2 = 17 - 6roo8/1 ( by rationalising the denominator we get this..)
1/x2 = 17 - 6root8
now,
x2 + 1/x2 = 17 + 6root8 + 17 - 6root8
x2 + 1/x2 = 34
then (x+1/x) square = x2 + 2 + 1/x square
(x+1/x) square = 34 + 2
(x+1/x) square = 36
then x+1/x = +6 or -6
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