The two numbers will be either 3 and 6 or -4 or -1.
Let the two numbers be x and y.
According to the given question.
The second number is three more tahn the first number.
⇒ y = x + 3 ...(i)
Also,
The product of the two numbers is 9 more than their sum.
⇒ xy = 9 + (x + y)
Substitute the value of y = x + 3 in xy = 9 + (x + y)
⇒ x(x + 3) = 9 + ( x + x + 3)
⇒ x^2 + 3x = 9 + 2x + 3
⇒ x^2 + 3x = 12 + 2x
⇒ x^2 + x - 12 = 0
⇒ x^2 + 4x -3x - 12 = 0
⇒ x(x + 4) -3(x + 4) = 0
⇒ (x - 3)(x + 4) = 0
⇒ x = 3 or x = -4
Therefore,
when x = 3
y = 6
and
when x = -4
y = -4 + 3
⇒ y = -1
Hence, the two numbers will be either 3 and 6 or -4 or -1.
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