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

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'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

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Substitute y=4 to equation 3

x = y + 5

x = 4 + 5

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Therefore the two numbers are 9 and 4.