Find the value of x, if 21^√x+20^√x = 29^√x.

Using Pythagoras theorem

a² + b² = c²

$21^{\sqrt{x}}+20^{\sqrt{x}} = 29^{\sqrt{x}}$

Compare the whole equation a² + b² = c²

So √x = 2

x = 4

21² + 20² = 29²

441 + 400 = 841

841 = 841

So x =  4 satisfy this equation