155052

Question: x^1/2+(1/x^1/2)<4. Find the ranges of x.
(x/x^1/2)+(1/x^1/2)<4

x+1/x^1/2<4

x+1<4(x^1/2)

Square both sides: (x+1)^2<16x

x^2+2x+1<16x

x^2-14x+1<0

If x^2-14x+1=0, we can find a range of values of x.

Using the quadratic formula- x= [14+(14^2-(4)(1)(1))^1/2]/2
x=(14+192^1/2)/2
=7+48^1/2
Answer: 0<(less than or equal to) x < 7+48^1\2
Side note: x must be positive as it is square rooted.