x2 -x -1 =0
2006-07-06 07:06:57 · 15 answers · asked by quicksilvergirl 3 in Science & Mathematics ➔ Mathematics
Solve this equation using the Quadratic Equation.. so a yahoo search for "quadratic equation" and you'll find several websites to explain it to you
This applies for almost any equation in the form ax^2 + bx +c = 0
(some do not have real answers)
x = [-b (+/-) sqrt (b^2 -4ac)]/2a
or in this case:
x = [-(-1) (+/-) sqrt(-1^2 -4(1)(-1))]/2 ==> [1 (+/-) sqrt(1-(-4))]/2
or [1 (+/-) sqrt(5)]/2
note that the (+/-) means Plus-or-Minus.. meaning that there are two roots.. one with [1 + sqrt(5)]/2 and one with [1-sqrt(5)]/2...
why two roots? well... what is sqrt(1)? most people answer immediately... 1... but -1 is also an answer.
When doing this Quadratic Equation, there are several types of answers... depending upon sqrt(???)... if ??? is < 0 then the solutions are imaginary, if ??? = 0 then both of the roots are the same value, and if ???> 0 then there are two real roots.
2006-07-06 07:34:49 · answer #1 · answered by ♥Tom♥ 6 · 0⤊ 0⤋
X=1
2006-07-06 07:17:14 · answer #2 · answered by thedude2005 3 · 0⤊ 1⤋
x=1
2006-07-06 07:08:32 · answer #3 · answered by Bean 3 · 0⤊ 1⤋
I assume this is a quadratic equation, x^2 - x - 1 = 0.
Others have given the correct answer, (1 +/- sqrt(5))/2.
Just an interesting addendum to this: the positive root here, (1+sqrt(5))/2, or about 1.618, is in fact phi, the golden ratio.
2006-07-06 11:00:08 · answer #4 · answered by Christopher S 2 · 0⤊ 0⤋
its actually 2x, but anyways: combine like terms, so basically 2x-x=x, there for x-1=0. This is where it gets confusing on a computer. You need to get x by itself. So add 1 to both sides, therefore x=1. (trust me, I'm right) Now test it: 2(1)-(1)-1=0, simplifies to 2-1-1=0
2006-07-06 07:13:47 · answer #5 · answered by Drew P 2 · 0⤊ 0⤋
I was never very good at Algebra. But I think x=1 Because 1minus itself is 0. So x=1
2006-07-06 07:11:57 · answer #6 · answered by Anonymous · 0⤊ 0⤋
x = to 1
x2 -x -1 = 0
becomes
x2 - x = 1
becomes
x2 = 1 + x
there for
2 x X = 1 + X
2 x 1 = 1 + 1
i coulda jst given you the answer because it was obvious just looking at the question, but though u may aswell learn how to do it
2006-07-06 07:13:05 · answer #7 · answered by Anonymous · 0⤊ 0⤋
since it is a quadratic equation n u cant split the middle term u use the formula..x= -b+-(b2-4ac)^1/2 the whole divided by 2a
where a,b and c are the coefficients of x2,x and 1
so they r 1,1 and 1
so the final answer is (1+root 5) by 2 and (1-root 5) by 2
2006-07-06 07:23:03 · answer #8 · answered by Barath 1 · 0⤊ 0⤋
The answer is not 1.
The fine and simple quadratic equation says...
x = [1 (+-) sq.5] / 2
2006-07-06 09:13:57 · answer #9 · answered by trancevanbuuren 3 · 0⤊ 0⤋
2x - x =0+1
x = 1
2006-07-06 07:33:49 · answer #10 · answered by danny 2 · 0⤊ 1⤋