Question 1102591
sqrt(5x)-sqr(2x)=3, put one sqrt on each side
sqrt(5x)=3+sqrt (2x)
square both sides
5x=9+6 sqrt(2x)+2x
3x-9=6 sqrt (2x) divide everything by 3
x-3=2 sqrt (2x)
square both sides
(x-3)^2=4*2x=8x
expand
x^2-6x+9=8x
x^2-14x+9=0
x=(1/2)(14+/- sqrt (196-36); sqrt (160)=12.65
x=(1/2)(26.65)=13.33
x=(1/2)(1.35)=0.68
check both
sqrt(3.4)-sqrt(1.36) does not equal 3
sqrt (66.65)-sqrt(26.66)=3  ANSWER is x=13.33
{{{graph(300,300,-10,20,-10,10,x^2-14x+9,sqrt(5x)-sqrt(2x)-3)}}} the steep slope is the roots of x^2-14x+9, and the shallow slope is the original equation minus 3, and the value of x is the result.  It equals 0 at 13.33