Question

(50 points)There are x ducks in a pond. The number of swans in the pond is equal to the square root of the number of ducks. If the total number of swans and ducks in the pond is 12, find the number of ducks.

Answer 1

The number of ducks are 9.

Explanation:

There are x ducks in a pond.

The number of swans in the pond is equal to the square root of the number of ducks.

Means swans =
`√(x)`

If the total number of swans and ducks in the pond is 12.

`x+ √(x) =12`

=>
`√(x) =12-x`

Squaring both sides, we get

`x=x^(2) +144-24x`

=> Taking everything on one side and equating to 0

`x^(2) -x-24x+144=0`

=>
`x^(2)-25x+144=0`

=> Solving this we get, x = 9 and x = -16

So, we have number of ducks as 9.

And number of swans =
`√(9) =3`