Question

The sum of two numbers is 45 and the mean proportional between them is 18. The numbers
are
a) (15, 30)
b) (32, 13
c) (36, 9)
d) (25, 20)
​

Answer 1

Step-by-step explanation:

x = first number

y = second number

x + y = 45 Subtract x to both sides

x + y - x = 45 - x

y = 45 - x

square root ( x * y ) = 18 Take square of both sides

x * y = 18 ^ 2

x * y = 324

x * ( 45 - x ) = 324

x * 45 - x * x = 324

45 x - x ^ 2 = 324 Subtract 324 to both sides

45 x - x ^ 2 - 324 = 324 - 324

45 x - x ^ 2 - 324 = 0

- x ^ 2 + 45 x - 324 = 0 Multiply by - 1

x ^ 2 - 45 x + 324 = 0

The solutions are :

x = 9 and x = 36

For x = 9

y = 45 - x = 45 - 9 = 36

For x = 36

y = 45 - x = 45 - 36 = 9

So numbers are 9 and 36

9 + 36 = 45

square root ( 9 * 36 ) = square root ( 324 ) = 18

P.S

If you don't know how to solve equation :

x ^ 2 - 45 x + 324 = 0