In the real number system,the equation $\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=1$ has how many solutions? In the real number system,the equation $\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=1$ has how many solutions?
I tried shifting the second term to the rhs and squaring.Even after that i'm left with square roots.No idea how to proceed.Help!

$$x+3-4\sqrt{x-1}=x-1+4-4\sqrt{x-1}=(x-1)-4\sqrt{x-1}+4=(\sqrt{x-1}-2)^2$$ Similarly $$x+8-6\sqrt{x-1}=(\sqrt{x-1}-3)^2$$ from which the answer.
It is not an equation but an identity in its domain of definition.This is the reason there are infinitely many solutions and not the expected finite number of them of a true equation with coefficients in a field. For example the "equation"
$$\sqrt[3]\frac{x^3-3x+(x^2-1)\sqrt{x^2-4}}{2}+\sqrt[3]\frac{x^3-3x-(x^2-1)\sqrt{x^2-4}}{2}=x$$ has all the reals as solutions.
