tanya
554/16
faridabad,haryana
2007-09-14 02:41:21 · 5 answers · asked by Tanyas 1 in Science & Mathematics ➔ Mathematics
x = 3 + root8
=> 1/x = 1 / ( 3 + root8 ) = ( 3 - root8 ) / ( 3^2 - 8 )
= 3 - root8
Now,
x^2 + ( 1/x )^2
= ( x - 1/x )^2 + 2
= ( 3 + root8 - 3 + root8)^2 + 2
= 34
You can take advantage of my free educational website www.schoolnotes4u.com when you are in XI/XII std.
2007-09-14 03:03:33 · answer #1 · answered by Madhukar 7 · 0⤊ 0⤋
xsquare+1/xsquare =
( 3 + 8^0.5)^2 + 1/( 3 + 8^0.5)^2 =
( 3 + 8^0.5)( 3 + 8^0.5) + 1/[( 3 + 8^0.5)( 3 + 8^0.5)] =
(9 + 3 * 8^0.5 + 3 * 8^0.5 + 8) + 1/(9 + 3 * 8^0.5 + 3 * 8^0.5 + 8) =
( 17 + 6* 8^0.5) + 1/( 17 + 6* 8^0.5) =
(multiple top and bottom of fraction by complement to get rid of radical in the denominator)
( 17 + 6* 8^0.5) + 1*( 17 - 6* 8^0.5)/( 17 + 6* 8^0.5)( 17 - 6* 8^0.5) =
( 17 + 6* 8^0.5) + ( 17 - 6* 8^0.5)/(289 - 36*8) =
( 17 + 6* 8^0.5) + ( 17 - 6* 8^0.5)/1 =
34
2007-09-14 10:08:37 · answer #2 · answered by Gary H 6 · 0⤊ 0⤋
(3 + sqrt(8))² = 17 + 6 sqrt(8)
1/x² = 1 / (17 + 6 sqrt(8))
= (17 - 6 sqrt(8)) / [(17 + 6 sqrt(8)) (17 - 6 sqrt(8))]
= (17 - 6 sqrt(8)) / (17² - 6² * 8)
= (17 - 6 sqrt(8))
then
x² + 1/x² = 17 + 6 sqrt(8) + 17 - 6 sqrt(8)
= 34
2007-09-14 10:08:22 · answer #3 · answered by Nestor 5 · 0⤊ 0⤋
(((3 + sqrt(8))^2) + 1) / ((3 + sqrt(8))^2) = 1.02943725
2007-09-14 09:54:42 · answer #4 · answered by {flick} 3 · 0⤊ 0⤋
17 + 6root8 + 1/(17 + 6root8)
But I am not sure how far you need to go.
2007-09-14 09:53:45 · answer #5 · answered by too_cute_n_sum 1 · 0⤊ 0⤋