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Find all pairs (r, s) such that 2s + r = 12 and rs = 3.     need answer today if possible please

Trinityvamp286  Jul 9, 2017
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 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

Guest Jul 9, 2017

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