Question

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

Answer 1

Answer:

Let the First Positive Number be n and Second Positive Number be (n + 3), as this Differ by 3.

$\underline{\bigstar\:\textsf{According to the Question :}}$

$\dashrightarrow\tt\:\:First\:No. \times Second\:No. =54\\\\\\\dashrightarrow\tt\:\:n(n+3)=54\\\\\\\dashrightarrow\tt\:\:n^2+3n=54\\\\\\\dashrightarrow\tt\:\:n^2+3n-54=0\\\\\\\dashrightarrow\tt\:\:n^2+(9-6)n-54=0\\\\\\\dashrightarrow\tt\:\:n^2 + 9n - 6n - 54 = 0\\\\\\\dashrightarrow\tt\:\:n(n + 9) - 6(n + 9) = 0\\\\\\\dashrightarrow\tt\:\:(n - 6)(n + 9) = 0\\\\\\\dashrightarrow\tt\:\:\underline{\boxed{ \green{\tt n =6 \quad} \tt or \quad \red{ n = - \:9}}}$

⠀

$\bullet\:\:\textsf{First Number = n = \textbf{6}}\\\bullet\:\:\textsf{Second Number = (n + 3) = \textbf{9}}$

Answer 2

Answer:

The numbers are 6 and 9.

Step-by-step explanation:

Let the smaller positive number be x.

And the greater number be (x + 3).

From the given condition,

x ( x + 3 ) = 54

∴ x² + 3x = 54

∴ x² + 3x - 54 = 0

∴ x² + 9x - 6x - 54 = 0

∴ x ( x + 9 ) - 6 ( x + 9 ) = 0

∴ ( x + 9 ) ( x - 6 ) = 0

∴ ( x + 9 ) = 0 OR ( x - 6 ) = 0

∴ x + 9 = 0 OR x - 6 = 0

∴ x = - 9 OR x = 6

But, the given number is positive.

∴ x = - 9 is unacceptable.

∴ x = 6

The smaller number ➔ x = 6

And the greater number ➔ x + 3 = 6 + 3 = 9

∴ The required numbers are 6 & 9.