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Question

Solve for :

       

The lower (or only) solution for this equation is    

The higher solution for this equation is    

The solution     is an extraneous solution (if any).

(Fill in each with an integer or a rational number or the word "none" or "n/a" with no capital letters or quotation marks.)

Answer 1

sqrt(5x+6)=3+sqrt(x+3)

5x+6=9+6sqrt(x+3)+x+3

4x-6=6sqrt(x+3)

16x^2-48x+36=36x+108

16x^2-84x-72=0 .... x=6, -.75

sub x=6 ... sqrt(5*6+6)=3+sqrt(6+3) ... 6=6, thus x=6 is a real solution

sub x=-.75 ... sqrt(-5*.75+6)=3+sqrt(-.75+3) ... sqrt(2.25)=3+sqrt(2.25) is not true ... thus x=-.75 is not real