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Identify 2 numbes with sum 14 and product 22

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timw996 | Student, Grade 10 | (Level 1) Salutatorian

Posted September 16, 2013 at 2:43 PM via web

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Identify 2 numbes with sum 14 and product 22

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 16, 2013 at 2:48 PM (Answer #1)

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Let the two numbers with sum 14 and product 22 be X and Y.

X + Y = 14

=> X = (14 - Y)

As the product is 22, X*Y = 22

=> (14 - Y)*Y = 22

=> 14Y - Y^2 = 22

=> Y^2 - 14Y + 22 = 0

=> `Y = (14 +-sqrt(196 - 88))/2`

=> `Y = 7 + 3*sqrt 3` and `Y = 7 - 3*sqrt 3`

X = `7 - 3*sqrt 3` and `X =7 + 3*sqrt 3 `

The two numbers are `(7 - 3*sqrt 3, 7 + 3*sqrt 3)` and `(7 + 3*sqrt 3,7 - 3*sqrt 3)`

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