# Find two numbers whose difference is 5 and the difference of their squares is 65 .involving quadratic equations

1
by jeanz143chess

2014-11-27T21:48:39+08:00
Let 'x' be the 1st number
'y' be the 2nd number
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-their difference is 5
x - y = 5    -----equation 1
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-the difference of their squares is 65
x² - y² = 65    ----equation 2
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From equation 1
x - y = 5
x = y + 5    ----equation 3
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Substitute equation 3 to equation 2
x² - y² = 65
(y+5)² - y² = 65
y² + 10y + 25 - y² = 65
10y + 25 = 65
10y = 65 - 25
10y = 40
y = 4
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Substitute y=4 to equation 3
x = y + 5
x = 4 + 5
x = 9
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Therefore the two numbers are 9 and 4.
How can we involve quadratic equation here.
http://www.algebra.com/algebra/homework/word/numbers/Numbers_Word_Problems.faq.question.214334.html .. like this ty.
Perhaps this equation (y+5)² - y² = 65.. it is a quadratic equation since its highest degree is 2. Perhaps you're thinking of quadratic formula? Well you're not asked to use quadratic formula but to have the expressions in quadratic equation. There's a difference between the two.
Ah thank you :)