x=3+sqroot of 8 find xsquare+1/xsquare?giv sortcut?

Answer 1

Answer is 34
which can be worked out as below

X= 3+ sq.rt of 8
X*2 = (3+sq.rt of8 )*2 = 9+ 2 x 3 x sq.rt.of 8 + 8
=17 + 6 x sq.rt of 8

similarly X*4 = ( X*2 ) *2 = 577 + 204 x sq.rt of 8

X*2 + 1 /X*2 = (X*4+ 1 ) / X*2

= (577 +1 + 204 x sq.rt.of 8) / 17 + 6 x sq.rt .of 8

= 578 + 576.912/(17 + 6 x 2.828)
= 1154.912/ (17 + 16.968 )
= 1154.912 / 33.968
= 34

Answer 2

if i understand the problem correctly, you want x^2+ 1/ x^2. ok this is how you do it (3+ sq root 8)^2= 9+6 sq root 8+ 8. that gives you 17 + 6 sq root 8, add that to 1/ 17 + sq root 8. you need to now do 17+ 6 sq root 8 under same denominator, so it becomes 289+ 12 sq root 8 + 288= 577+ 12 sq root 8/(17+6 sq root 8)+ 1/ 17+ sq root 8. result should be 578+12 sq root 8/ (17+ 6 sq root 8).... thats it

Answer 3

x = 3 + sqrt8
x^2 + 1/x^2 = (3+sqrt8)^2 + 1/(3+sqrt8)^2 =
9 + 6sqrt8 + 8 + 1/(9+6sqrt8+8) =
17 + 12sqrt2 + 1/(17+12sqrt2) =
17 +12sqrt2 +(17-12sqrt2)/((17+12sqrt2)(17-12sqrt2)) =
17 + 12sqrt2 +(17-12sqrt2)/(289-12) =
17 + 12sqrt2 + (17-12sqrt2)/275

If you like that all as one fraction, it's
(276*17 + 274*12sqrt2)/275

Answer 4

Given x = 3+sqroot of 8

= 3+2.83 = 5.83

x^2 = 33.99

x^2+1/x^2 = 33.99+1/33.99

= 34 (approx)

Answer 5

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Answer 6

X = 3 + sq.root of 8
X = 3 + 2.828
X = 5,828


Now

X^2 + 1/X^2
= 5.828 + 1/5.828
= 5.828 + 0.172
= 6