Question

HELP ME ASAP PLEASEE!!

Solve the radical equation AND find the extraneous solutions: √(2x + 3) = x

Answer 1

`(x+1)(x-3)=0\\x=-1,3\\√(2(-1)+3)=-1\\ √(1)=-1\\ √(2(3)+3)=3\\ √(9)=3\\`

There are no extraneous solutions

Explanation:

To solve this equation, first we want to cancel out the radical;

`(√(2x+3) )^2=x^2; 2x+3=x^2`

Now that the equation looks simpler, we can slide 2x+3 to the other side to create a polynomial that we can factor;

`x^2-2x-3=0\\(x+1)(x-3)=0`

You can check for extraneous solutions by plugging the answers in, which I showed above.