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Find two positive numbers whose difference is 20 and whose product is 189 .

User Zword
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Final answer:

The two positive numbers whose difference is 20 and whose product is 189 are 27 and 7, found by setting up a system of equations and solving them step-by-step.

Step-by-step explanation:

To find two positive numbers whose difference is 20 and whose product is 189, we can set up a system of equations:

  • x - y = 20
  • xy = 189

By solving these equations, we find the numbers to be x = 21 and y = 1.

Step 1: From the first equation, we express one variable in terms of the other, x = y + 20.
Step 2: Substitute x in the second equation, (y + 20)y = 189.
Step 3: Expand the equation and solve the quadratic, y2 + 20y - 189 = 0.
Step 4: Factor the equation, (y - 7)(y + 27) = 0.
Step 5: Two possible solutions for y are y = 7 or y = -27. Since we need positive numbers, we take y = 7.

Step 6: Substitute y back into x = y + 20 to find x, x = 7 + 20 = 27.

Therefore, the two positive numbers are 27 and 7.

User Nam Duong
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