by barnamah » Sun 03 April, 2011 15:32
to solve `x^2 - x - 1 = 0` we use quadratic equation:
`x_(1,2)=(-b+-sqrt(b^2+4ac))/(2a)`
in our equation `x^2 - x - 1 = 0` in the form `ax^2+bx+c=0`
a=1 (a is the coefficient of `x^2`, `ax^2`)
b=-1 (b is the coefficient of of -x which is -1)
c=-1 (c is the last terms -1)
sub in the values and we have:
`x=(-(-1)+-sqrt((-1)^2+4(1)(1)))/(2(1))=(1+-sqrt(1+4))/(2)`
Now we have `+-` in our equation so we have to solve this twice as follow:
`x=(1+sqrt(1+4))/(2)=1.61803398`
and `x=(1-sqrt(1+4))/(2)=-0.61803398`
`:.` x=1.61803398 and x=-0.61803398
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