Okay that is not maths for capable of doing in the summer.
If you tell us what u need this for, I'll give it a try.
Formerly known as gamer4evere
I'm going to do my best typing this up. I'm bound to fuck up somewhere with the parenthesis but the basic steps should be easy for you to get on your own.
Firs you want to eliminate any square roots on the left that you can. Do this by squaring both sides.
√x+(√x+4)^2 = 4+2x+(2√x)(√x+4) = 4+2 x+2√(x(x+4)) = ((√x+1)+(√x+2))^2
You'll end up with:
4+2x+(2√x(x+4)) = (√(x+1)+√(x+2))^2
Now you want to get rid of that radical on the left (4+2x), do this by subtracting it from both sides:
2√(x(x+4)) = (√(x+1)+√(x+2))^2-4-2x
Now you can get rid of yet another square root, do so by squaring again:
4x(x+4) = ((√(x+1)+√(x+2))^2-4-2 x)^2
Now you can see that you can simplify the left hand side:
4x^2+16x = ((√(x+1)+√(x+2))^2-4-2 x)^2
You can also do the same for the right side.
((√(x+1)+√(x+2))^2-4-2x)^2 = 9+12 x+4 x^2-4√(x+1)√(x+2):
4 x^2+16x = 9+12 x+4x^2-4 √(x+1) √(x+2)
You can also shove √(x+1) and √(x+2) under the same square root:
4x^2+16x = 9+12x+4x^2-4√((x+1)(x+2))
Here's the trickiest part in my opinion. You're gonna hit two birds with one stone by subtracting 4x^2 + 16x - 4√((x+1) (x+2)) from both sides.
So now 4x^2+16x = 9+12x+4x^2-4√((x+1)(x+2))
becomes
4√((x+1)(x+2)) = 9-4x
Oh look now we have another square root. Let's square this shit again:
16(x+1)(x+2) = (9-4x)^2
Simplify that motherfucker on the left:
16x^2+48x+32 = (9-4x)^2
Simplify the motherfucker on the right hand side:
16 x^2+48 x+32 = 16x^2-72 x+81
Now take everything on the right and shove it over to the left by subtracting 16x^2-72 x+81 from both side:
120x-49 = 0
Now we can put that 49 over to the right:
120x = 49
Holy shit, now divide both sides by 120 and what do you have?:
x = 49/120
FUCKING MATHS BITCH
---------- Post added at 08:40 PM ---------- Previous post was at 08:39 PM ----------
Fuck you I wrote a step by step for no reason
Deflorate. (08-01-2013),Plutonsvea (08-01-2013),WarWood (08-01-2013)