Question

The difference between 2 numbers is 20 and their product is 125. What are 2 numbers.​

Answer 1

Let the 2 numbers be x and y.

Then according to question,

$\begin{gathered} \sf \:x - y = 20 \\ \sf so, x = y + 20 \\ \\ \sf \dashrightarrow x \times y = 125 \\ \sf \dashrightarrow \: (y +20)\times y = 125 \\\sf \dashrightarrow y^2 + 20y =125 \\ \sf \dashrightarrow \: y^2 + 20y - 125 = 0\\\sf \dashrightarrow y^2 + 20y - 125 = 0 \\\\\sf \dashrightarrow y^2 + 25y - 5y - 125 = 0\\ \sf \dashrightarrow y(y + 25) - 5(y + 25) = 0\\ \sf \dashrightarrow (y -5) (y + 25)= 0 \\ \sf \dashrightarrow so, y = 5 , -25 \\ \\\rm then,\\ \rm x = y +20\\ y = 25 ,-5\end{gathered}$

The two numbers are ( -25 , -5 ) or ( 5 , 25 )

$\rule{300px}{.7ex}$

Answer 2

Given : The difference between 2 numbers is 20 and their product is 125.

To Find : What are 2 numbers.​

Solution:

Assume that 2 numbers are x  and x + 20

Product = 125

=> x ( x + 20) = 125

=> x²  + 20x  = 125

=> x² + 20x - 125 = 0

=> (x + 25 ) (x - 5) = 0

=> x = - 25  and  x = 5

x = - 25  => x + 20  = -25 + 20 = - 5

x = 5 => x + 20  = 5 + 20 = 25

Hence numbers are  ( -25 , -5 )

or ( 5 , 25 )

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