Q. 54.8( 4 Votes )

Two positive numbers differ by 3 and their product is 54. Find the numbers.

Let the two numbers be x and y.

According to the question,

x – y = 3 …(i)

Also, x×y = 54

…(ii)

On putting the value of in Eq. (i), we get

54 – y2 = 3y

y2 + 3y – 54 = 0

y2 + 9y – 6y – 54 = 0

y(y + 9) – 6(y + 9) = 0

(y – 6)(y + 9) = 0

y = – 9 and 6

But y = – 9 can’t be the one number as it is given that the numbers are positive.

Hence, the two numbers are 9 and 6.

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