(x^1/2) + (x^1/4) = 20
Let x^1/4 = a-----------------(1)
square of (1); x^1/2 = a^2 --------(2)
Now equation becomes a^2 + a = 20
a^2 + a -20 = 0
a*a + 5a - 4a -20 =0
a( a + 5) -4 (a+ 5) = 0
(a +5 ) (a - 4) = 0
a +5 = 0 or a -4 =0
a = -5 or a = 4
x^1/4 = -5 or x^1/4 = 4 { from (1) }
x = ( -5 )^4 or x = (4 )^4 { raised power 4 bothsides }
x = 5^4 or x = 4^4
x = 5*5*5*5 or x = 4*4*4*4
x =625 or x = 256