Two Values of X
Date: 03/20/2002 at 00:13:28 From: Krystal Subject: Word problem Two numbers differ by 7 and the sum of their squares is 389. Find the two numbers. I set up the equation as 389 = (x) squared + (x-7) squared, but I can't get two true answers. Can you help me?
Date: 03/20/2002 at 01:45:57 From: Doctor Jeremiah Subject: Re: Word problem Hi Krystal, I think the problem is that you are misinterpreting the answer that you are getting. Your equation "389 = (x) squared + (x-7) squared" is correct. 389 = (x) squared + (x-7) squared 389 = (x) squared + (x) squared - 14x + 49 389 = 2 (x) squared - 14x + 49 0 = 2 (x) squared - 14x + 49 - 389 0 = 2 (x) squared - 14x - 340 0 = (x) squared - 7x - 170 Now we must solve this quadratic for x. If we use the quadratic formula: x = ( -b +- squareroot( (b) squared - 4ac ) ) / (2a) Then a = 1, b = -7 and c = -170 and we get: x = ( -(-7) +- squareroot( (-7) squared - 4(1)(-170) ) ) / (2(1)) x = ( 7 +- squareroot( 49 + 680 ) ) / 2 x = 7/2 +- squareroot( 729 )/2 x = 7/2 +- 27/2 x = 34/2, x = -20/2 x = 17, x = -10 So now you are thinking, these two values of x do not differ by 7. Well, they aren't supposed to. The two numbers that differ by 7 are x and x-7. It just turns out that there are two possible sets of numbers that differ by 7. Each value of x has a corresponding value for x-7. The first answer is: x = 17 and x-7 = 17-7 = 10 And the other answer is: x = -10 and x-7 = -10-7 = -17 So there are two sets of numbers that differ by 7 that could be answers to the question. Usually the question reads "two POSITIVE numbers that differ by ..." and you would pick the first set, but the question does not exclude either set, so you can pick whichever one you want. - Doctor Jeremiah, The Math Forum http://mathforum.org/dr.math/
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