It is a question from algebraic identities.
2007-12-15 12:55:04 · 10 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
x+1 = 6x
5x = 1
x= 1/5
plug that into the 2nd equation
=(1/5)^2 + (5^2)
=1/25 +25
2007-12-15 12:58:59 · answer #1 · answered by ¿ /\/ 馬 ? 7 · 0⤊ 4⤋
well, wen u say x2, hope fully it means x squared? next time, remember that x squared (or any power) can be written with ^.
x+1/x=6
lets make 1/x y instead of 1/x. so:
x+y=6
y=1/x
from the second equation, we know:
x*y=1
from the first equation, we know:
x=6-y
thus:
(6-y)*y=1
6y-y^2=1
bring this into the standard form:
-y^2+6y-1=0
lets factor it.
two numbers that wen multiplied u get 1 and wen u add, u get 6.
well, thats basically wat we started out with!
any way, lets use the other way to solve.
y=(-6+/-â(6^2-4(-1)(-1)))/2(-1)
y=(-6+/-â(36-4)/-2
y=(-6+/-â32)/-2
â32 is about 5.66
y=(-6+/- 5.66)/-2
first value:
y=(-6+5.66)/-2
y=-.34/-2
y=.17
second value:
y=(-6-5.66)/-2
y=-11.66/-2
y=5.83
input the first value into first or second equation:
.17+x=6
x=6-.17
x=5.83
insure it fits in second equation:
(5.83)(.17)=1
u shud get .9911, a reasonable answer since we estimated.
as u can see, the second value of y is the first value of x, so it is useless to input this, because the result will be backwards.
so,
x=.17
y=5.83
y=1/x
thus, x^2+1/x^2= still about (.17)^2+1/(.17)^2=.0289+1/.0289=34.63
these were all estimations, so do not worry if it is a few decimals off.
2007-12-15 21:36:56 · answer #2 · answered by Harris 6 · 1⤊ 0⤋
x+1/x = 6
x +1 = 6x
5x = 1
x = . 2
.2 + 1 / .2 = 6
x = .2
.2^2 + 1/.2^2 = .04 + 1 / .04 = 25.04
2007-12-15 21:17:45 · answer #3 · answered by ViewtifulJoe 4 · 0⤊ 1⤋
First, find X
X+1/X = 6
X+1 = 6X
X+1-6X = 0
5X+1 = 0
5X = -1
X = -1/5
Now, substitute X with -1/5 in the other equation:
(-1/5)*2 + 1/((-1/5)*2) = X
(-2/5) + 1/(-2/5) = X
-2.9=X
2007-12-15 21:04:07 · answer #4 · answered by lenardz33 3 · 0⤊ 2⤋
x+1/x = 6
x+1 = 6x
5x = 1
x = 1/5 or 0.2
x2+1/x2 =
(0.2)2 + 1/(0.2)2
=25.04
2007-12-15 21:00:23 · answer #5 · answered by awkwardzombie 3 · 0⤊ 3⤋
solve for x first....
x +1 = 6x
x = 1/5
substituting...
1/25 + 1/(1/25) = 1 1/25
2007-12-15 21:00:22 · answer #6 · answered by jamesyoy02 6 · 0⤊ 3⤋
(x + 1/x)^2 = x^2 + 2 + 1/x^2 = 36
x^2 + 1/x^2 = 34
2007-12-15 20:58:10 · answer #7 · answered by norman 7 · 4⤊ 3⤋
-2.9
This answer is actualy correct even though they give me thumbs down.
2007-12-15 20:59:37 · answer #8 · answered by Anonymous · 0⤊ 4⤋
bout tree fitty
2007-12-15 20:58:06 · answer #9 · answered by nickwootwoot 2 · 0⤊ 6⤋
x = poop
2007-12-15 20:57:40 · answer #10 · answered by Anonymous · 0⤊ 6⤋