We have to find the values of x that satisfy: 4x^2 -4x -1 = 0
For a quadratic equation the roots can be expressed as
x1 = [-b + sqrt (b^2 - 4ac)]/2a
=> [4 + sqrt ( 16 + 16)]/8
=> 1/2 + sqrt 2 / 2
x2 =...
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We have to find the values of x that satisfy: 4x^2 -4x -1 = 0
For a quadratic equation the roots can be expressed as
x1 = [-b + sqrt (b^2 - 4ac)]/2a
=> [4 + sqrt ( 16 + 16)]/8
=> 1/2 + sqrt 2 / 2
x2 = x1 = [-b + sqrt (b^2 - 4ac)]/2a
=> 1/2 - sqrt 2 /2
The values of x which satisfy 4x^2 -4x -1 = 0 are 1/2 + sqrt 2 / 2 and 1/2 - sqrt 2 / 2.
Given the quadratic equation 4x^2 -4x -1 =0
We need to find the solution or the roots of the equation.
We will use the quadratic formula.
==> a = 4 b= -4 c = -1
==> x = (-b + - sqrt(b^2 -4ac)/ 2a
==> x1 = (4 + sqrt(16-4*4*-1) / 2*4
= (4+sqrt(32) / 8
= (4+ 4sqrt2)/8 = (1/2) + sqrt2 /2
==> x1= (1/2) + sqrt2 / 2
==> x2 = (1/2) - sqrt2 / 2