HELP!

how do I solve this?
the square root of x equals the square root of (x-5) +1

Question

HELP!

how do I solve this?
the square root of x equals the square root of (x-5) +1

mathmate · Answer

Just confirming:
$ \sqrt{x} = \sqrt{x-5} + 1$
Is this the equation?

anonymous · Answer

square twice and get the solution

mathmate · Answer

You can use trial and error.  The answer is a small integer.

anonymous · Answer

sqrt(x)=sqrt(x-5)+1
sqrt(x)-1=sqrt(x-5)
squaring both sides
x+1-2*sqrt(x)=x-5
2*sqrt(x)=6
sqrt(x)=3
x=9

mathmate · Answer

Also note that the difference of two consecutive squares is an odd number:
5^2-4^2=9
4^2-3^2=7
3^2-2^2=5
2^2-1^2=3
...

anonymous · Answer

yes mathmate thats right

anonymous · Answer

$$here x \ge 0, x \ge 5 ,so x \ge 5$$
$$x=\left( x-5 \right)+2\sqrt{x-5}*1+1$$
$$2\sqrt{x-5}=x-x+5-1=4$$
$$\sqrt{x-5}=2$$
again squaring x-5=4,x=9

anonymous · Answer

Thanks So Much!!!

anonymous · Answer

yw