How do you find two positive numbers such that the sum of the squares of the two numbers is 169 and the difference between the two numbers is 7?

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Answer 1 · 2016-12-11T06:59:58

5, 12

Let #x# be the larger of the 2 positive numbers
Let #y# be the smaller of the 2 positive numbers

#x^2 + y^2 = 169#

#x - y = 7#

#=> x = 7 + y#

#x^2 + y^2 = 169#

#=> (y + 7)^2 + y^2 = 169#

#=> y^2 + 14y + 49 + y^2 = 169#

#=> 2y^2 + 14y - 120 = 0#

#=> 2(y^2 + 7y - 60) = 0#

#=> y^2 + 7y - 60 = 0#

#=> (y + 12)(y - 5) = 0#

#=> y = -12, y = 5#

However, we want #y > 0#

#=> y = 5#

#x - y = 7#

#=> x - 5 = 7#

#=> x = 12#