Question

What numbers have the diffrence of 20 and pruduct of 125

Answer 1

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Let the 2 numbers be x and y.

The difference between 2 numbers is 20.

$\begin{gathered} \sf \: x - y = 20 \\ \\ \sf \dashrightarrow x = 20 + y\end{gathered}$

The product of 2 numbers is 125.

$\begin{gathered} \sf \: xy = 125 \\ \\ \sf \dashrightarrow \: (y + 20)y = 125 \\ \\ \sf \dashrightarrow {y}^{2} + 20y = 125 \\ \\ \sf \dashrightarrow \: {y}^{2} + 20y - 125 = 0 \\ \\\sf \dashrightarrow {y}^{2} + 25y - 5y - 125 = 0 \\ \\ \sf \dashrightarrow \: y(y + 25) - 5(y + 25) = 0 \\ \\\sf \dashrightarrow (y - 5)(y + 25) = 0 \\ \\\sf \therefore \red{y = 5 \: and \: - 25}\end{gathered}$

The two numbers are 5 and -25.

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Answer 2

Let the 2 numbers be x and y.

The difference between 2 numbers is 20.

$\begin{gathered} \sf \: x - y = 20 \\ \\ \sf \dashrightarrow x = 20 + y\end{gathered}$

The product of 2 numbers is 125.

$\begin{gathered} \sf \: xy = 125 \\ \\ \sf \dashrightarrow \: (y + 20)y = 125 \\ \\ \sf \dashrightarrow {y}^{2} + 20y = 125 \\ \\ \sf \dashrightarrow \: {y}^{2} + 20y - 125 = 0 \\ \\\sf \dashrightarrow {y}^{2} + 25y - 5y - 125 = 0 \\ \\ \sf \dashrightarrow \: y(y + 25) - 5(y + 25) = 0 \\ \\\sf \dashrightarrow (y - 5)(y + 25) = 0 \\ \\\sf \therefore \red{y = 5 \: and \: - 25}\end{gathered}$

The two numbers are 5 and -25.

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