Exponent and radicals solve for x and check: sqrt of 12 + x = 2 + sqrt of x?

Answer 1

(12+x)^.5 = 2 + sqrtx
square both sides

12+x = 4+ 4sqrtx + x
8=4sqrtx
x=4

Do not make it harder than it is.

Answer 2

I think that you mean sqrt (12+x)

sqrt x exists iff x>=0

sqrt (12+x) exist iff x+12 >=0, so, of x>=0, it exists,

Now lets solve this.

sqrt (x+12) >=0

And 2 + sqrtx >=0 too, so you can square this expression without introducing roots.

You get this:

12 + x = 4 + 2*2*sqrt x + x

Then cancel x and substract 4 to the 12

You get this:

8 = 4 sqrt x

sqrt x = 2

x = 4

Ana

Answer 3

sqrt(12)+x=2+sqrt(x)
x-sqrt(x)+sqrt(12)-2=0
the simplest way is to let y=x^2 so
y^2-y+2(sqrt(3)-1)=0
y=(1+/-sqrt(1-4*1*(2(sqrt(3)-1)))/2
plug in & solve. then x=sqrt(y)