Find all pairs (r, s) such that 2s + r = 12 and rs = 3. need answer today if possible please
2s + r = 12 and rs = 3.
r =3/s sub in the 1st equation and solve for s
Solve for s:
2 s + 3/s = 12
Bring 2 s + 3/s together using the common denominator s:
(2 s^2 + 3)/s = 12
Multiply both sides by s:
2 s^2 + 3 = 12 s
Subtract 12 s from both sides:
2 s^2 - 12 s + 3 = 0
Divide both sides by 2:
s^2 - 6 s + 3/2 = 0
Subtract 3/2 from both sides:
s^2 - 6 s = -3/2
Add 9 to both sides:
s^2 - 6 s + 9 = 15/2
Write the left hand side as a square:
(s - 3)^2 = 15/2
Take the square root of both sides:
s - 3 = sqrt(15/2) or s - 3 = -sqrt(15/2)
Add 3 to both sides:
s = 3 + sqrt(15/2) or s - 3 = -sqrt(15/2)
Add 3 to both sides:
Answer: | s = 3 + sqrt(15/2) r = 6 - sqrt(30) ≈ 0.522774 s = 3 - sqrt(15/2) r = 6 + sqrt(30) ≈ 11.4772