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the square root of the difference between the squares of two positive numbers is 4. if the number differ by 2, what are the numbers?​

Sagot :

Let x and y be the 2 numbers

According to the given , we know that

√( x^2 - y^2) = 4

y = x - 2

or

x = y - 2

Next is we do substitution , lets do y = x-2 first

√[x^2 - (x - 2)^2 ] = 4

x^2 - x^2 + 4x - 4 = 16

4x = 20

x= 5

then find y

y= 5 - 2

y = 3

Next is we do substitute if x = y - 2

√[(y - 2)^2 - y^2] = 4

y^2 - 4y + 4 - y^2 = 16

-4y = 12

y= - 3

Since it says "positive" x= y-2 is not a solution since we got y as negative

so answer ? 5 and 3