I have been doing good so far with these problems but I have hit a road block and just can't seem to get pass it. The problems is as follows:
equation is 2x^24x+5=0 and the roots are a and b. I am suppose to finde the value of 1/(a+1) + 1/(b+1). I have already fond that a+b= b/a = (4/2)= 2 and ab=c/a=5/2. Is there anyone out there who can help me?
2x^2  4x + 5 = 0, dividing BOTH SIDES by 2, we have x^2  2x + 5/2 = 0
a + b = 2 and ab = 5/2
Or as suggested by SKEETER: evaluate this . . . .
= [(a + b) + 2]/[(ab) + (a + b) + 1] = [2 + 2]/[5/2 + 2 + 1] = 4/[5/2 + 3] = 4/[11/2] = 8/11.
Or THIS,
x^2  2x + 5/2 = 0, let x = y  1, so that the root will be x + 1
(y  1)^2  2(y  1) + 5/2 = 0,
y^2  2y + 1  2y + 2 + 5/2 = 0,
y^2  4y + 3 + 5/2 = 0
y^2  4y + 11/2 = 0.
let y = 1/z, so that the root will be 1/(x + 1),
(1/z)^2  4(1/z) + (11/2) = 0, multiply both sides by (2/11)z^2,
2/11  (8/11)z + z^2 = 0, rearranging,
z^2  (8/11)z + 2/11 = 0,
notice that the sum of roots is 8/11.
