Question

Show me how to do this step by step. Let me put the equation on the 2nd post.

Answer 1

equation?

Answer 2

\[\sqrt{5x+4}-1=\sqrt{3x+1}\]

Answer 3

Square both sides of the equation
\[5x+4-2\sqrt{5x+4}+1=3x+1 \implies 2x+3=2\sqrt{5x+4}\]
Square both sides of the equation again
\[4x^2+12x+9=4(5x+4)\]
This is a quadratic equation now, I think you can do it.

Answer 4

hmmm....i got the quad. equation as 4x^2-20x+8=0...
and so x shud be (5+sqrt17)/2, (5-sqrt17)/2

Answer 5

hm okay

Answer 6

anymore hints? i'm not getting this at all.

Answer 7

I made a slight mistake above. We had
\[5x+4-2\sqrt{5x+4}+1=3x+1\implies 2x+4=2\sqrt{5x+4}.\] Squaring both sides gives:
\[4x^2+16x+16=4(5x+4) \implies 4x^2+16x+16=20x+16 \]
\[\implies 4x^2-4x=0 \implies 4x(x-1)=0 \implies x=0 \text{ or }x=1.\]
Now you need to check each solution by plugging into the original equation.
At x=0, we get 1=1, which is true.
At x=1, we have 2=2. so x=1 is also a solution.