Question

The difference between two numbers is 9 and the product of the numbers is 162
Activity 17
Find the two numbers,​

Answer 1

Answer:

Let the two numbers be x and y

$x - y = 9 \\ \\ \\ xy = 162 \\ \\ \\ {(x - y)}^{2} = {(9)}^{2} \\ \\ \\ {x}^{2} + {y}^{2} - 2xy= 81 \\ \\ \\ {x}^{2} + {y}^{2} - 2 \times 162 = 81 \\ \\ \\ {x}^{2} + {y}^{2} = 81 + 324 \\ \\ \\ {x}^{2} + {y}^{2} = 405$

Answer 2

Answer is 18 and 9 OR -9 and -18 respectively

x-y= 9
x= 9+y....(1)
Also x.y=162....(2)
(1) in (2)
y(9+y)= 162
y^2+ 9y-162=0
y^2-9y+18y-162=0
y(y-9)+18(y-9)=0
(y+18)(y-9)=0
Y=-18 or Y=9

When Y=-18, x=9-18 From (1)
x=-9
When Y=9, x=9+9 From (1)
x=18