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Old 07-30-2007   #4
Shobiz
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This process is much simpler. Please notice the steps and you'll understand what I'm saying.Let the two unknown numbers be 'a' and 'b'.According to the question;1) a+ b = 452) (a/b) + (b/a) = 2.05Solving 2);(a/b) + (b/a) = 2.05=> (a^2 + b^2)/ (ab) =2.05=> (a + b)^2 -2ab = 2.05 (ab)NOTE: a^2 + b^2 = (a+b)^2 -2ab Now, we'll use, 1) a+b = 45;=> (45)^2 -2ab = 2.05ab=> 2025 = 4.05ab=> ab = 2025/4.05 = 500 (This is the product of the two unknown variables).Now, (a-b)^2 = (a+b)^2 -4ab = (45)^2 - 4(500) = 2025 -2000 = 25Therefore, (a-b) = + or - 5 Now, taking case a);a+b =45a-b = 5Soliving the above two equations, we get;a = 25b =20 Taking case b);a+b =45a-b = -5On solving these two equations, we get;a = 20b =25Therefore, the two numbers are 20 and 25 and the product is 500.
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