the-system-of-equation-a-c-2-1-16-b-2-1-16-b-a-2-1-25-c-2-1-25-c-b-2-1-36-a-2-1-36-given-that-a-b-c-are-real-number

Question Number 11831 by Peter last updated on 02/Apr/17

the system of equation

a - \sqrt{c^{2} - \frac{1}{16}} = \sqrt{b^{2} - \frac{1}{16}}

b - \sqrt{a^{2} - \frac{1}{25}} = \sqrt{c^{2} - \frac{1}{25}}

c - \sqrt{b^{2} - \frac{1}{36}} = \sqrt{a^{2} - \frac{1}{36}}

given that a, b, c are real numbers

that satisfy they system of equation \dots

if a + b + c = \frac{x}{\sqrt{y}} where x, y are

positive integers and y is square free

find the value of x + y