My thought process on how I solved this: Since Kaiju wants a nice solution, I'll try sqrt(x) natural and sqrt(x + 15) natural: we get x = 1. Plugging that in, we get a correct solution. Since the left side is monotonically increasing and the right side is monotonically decreasing, that must be the only solution.
My thought process on how I solved this:
Since Kaiju wants a nice solution, I'll try sqrt(x) natural and sqrt(x + 15) natural: we get x = 1.
Plugging that in, we get a correct solution.
Since the left side is monotonically increasing and the right side is monotonically decreasing, that must be the only solution.
Interesting! Didn’t think about the increasing or decreasing.
How I solved it (without watching the video first, of course):
√x + √(x+15) = 5/√x | - √x
√(x+15) = 5/√x - √x
√(x+15) = 5/√x - x/√x
√(x+15) = (5-x)/√x | * √x
√(x+15) * √x = 5-x | ()²
(x+15) * x = (5-x)²
x² + 15x = 25 - 10x + x² | - x²
15x = 25 - 10x | + 10x
25x = 25 | * (1/25)
x = 1
Interesting approach! Cool! Thanks for sharing!
x+√(x)√(x+15)=5 and x≠0
5-x=√(x)√(x+15)
25-10x+x²=x²+15x
25-25x=0
x=1
1+√16=5/√1, this is indeed true.
x=1.
Sick! Way to go!