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

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Charlotte12viz

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

x-y= 5

x^2-y^2= 65

 

x-y= 5

x= 5 +y

x^2= (5 +y) (5 +y)

x^2= (25 + 5y +5y+ y^2)

x^2= 25 + 10y+ y^2

 

x^2-y^2= 65

25 + 10y+ y^2-y^2= 65

25 + 10y = 65

10y = 65-25

10y = 65-25

10y = 40

10y/10 = 40/10

y=4

 

x-y= 5

x-4= 5

x= 5+4

x= 9

 

x^2-y^2= 65

9^2-4^2= 65

81-16=65

65=65

 

Answer:

x= 9

y=4