Olympiad | The square root of x + the square root of y = the square root of 80;Can you find x and y?

[@nasrullahhusnan2289]

sqrt(x)+sqrt(y)=sqrt(80)
=4sqrt(5)
=[k+(4-k)]sqrt(5)
for any 0=

[@2sljmath]

Sqrt(x)=K.sqrt(5)==>x=(k^2).5
Sqrt(y)=(4--k)sqrt(5)==>y=((4--k)^2).5
K=1,2,3
So:
x=45 , y=5
x=5 , y=45
x=20 , y=20
Thank you.

[@gregevgeni1864]

For x = 0 => y = 80 => (x , y) = (0 , 80) solution.
By symmetry (x , y) = (80 , 0) is another solution.

[@2sljmath]

But zero is not a natural number!

[@gregevgeni1864]

I apologize, but it is not mentioned that x and y are natural numbers.

[@tomycarmo4]

​@@gregevgeni1864 It is shown that X and Y are natural numbers at the very start of the video.

[@mathisdesaveur3259]

Why is 80 = 16.5?

[@2sljmath]

Because:
80= 16×5
and:
16^(1/2)=4