1 = sqrt(x^2 +y^2)
dont understand why
dont understand why

x² is always positive..
y² is also always positive..
sp √(x²+y²) is always positive..
SO it can't equal 1
y² is also always positive..
sp √(x²+y²) is always positive..
SO it can't equal 1

When you have √, ALWAYS take principal square root (i.e. positive square root)
So left side = 1 < 0, but right side >= 0
Therefore there is no solution.
====================
Please note that in quadratic formula: x = (b ± √(b²4ac)) / (2a)
we EXPLICITLY use ± in front of square root, since there is a difference
between √(b²4ac) and √(b²4ac)
Example:
√64 = 8
√64 = 8
So left side = 1 < 0, but right side >= 0
Therefore there is no solution.
====================
Please note that in quadratic formula: x = (b ± √(b²4ac)) / (2a)
we EXPLICITLY use ± in front of square root, since there is a difference
between √(b²4ac) and √(b²4ac)
Example:
√64 = 8
√64 = 8

actually solutions exist
on squaring both sides
1 = x^2 +y^2
The solutions are (0,1);(1,0);(0,1);(1,0)
The equation represents a circle with radius 1
on squaring both sides
1 = x^2 +y^2
The solutions are (0,1);(1,0);(0,1);(1,0)
The equation represents a circle with radius 1

1 = x^2 + y^2 this represent circle of radius 1 & center (0,0) on xy plane
so any x,y value on circle is a solution for equation
so any x,y value on circle is a solution for equation

a solution does exist
x = 1
y = 0
whoever told you no solutions exist is wrong
x = 1
y = 0
whoever told you no solutions exist is wrong

thanks