We square the assumed formula

y = [root]a + [root]b + [root]c,

and obtain

y^2 = a + b + c + 2([root]ab + [root]ac + [root]bc);

or, substituting -P for a + b + c, and transposing,

y^2 + P = 2([root]ab + [root]ac + [root]bc).