show that 5+x-(square root of 3+4x=0) has no solutions

Question

Square root

Answer 1

5+x-sqrt(3+4x)=0;

(5+x)^2=3+4x;

25+10x+x^2=3+4x;

x^2+6x+22=0. Using the formula we have as the discriminant 36-88 which is negative, so the square root cannot exist as a real number. Therefore there are no solutions, and this can be seen from the graph of the quadratic expression, which doesn't intercept the x axis.