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√x+ 1/(√x) <4

Simplify left left hand side to give ((√x)^2+1)/(√x)<4 then further simplification gives (x+1)/(√x)<4

Multiply both sides by √x leaving the inequality x+1<4√x

Square both sides to remove the square root: x^2+2x+1<16x then subtract 16x from both sides , resulting in x^2-14x+1<0.

Since this inequality cannot be factorised easily, I changed
the less than sign to an equal sign and applied the quadratic formula, substituting in a=1,b=-14 and c=1: x=(-b±√(b^2-4ac))/2a=(-(-14)±√((-14)^2-4(1)(1)))/(2(1))

When simplified this leaves x=7-4√3 or x=7+4√3

Therefore the range of values for x which satisfy the inequality is 7-4√3<x<7+4√3