(a) 1
x2 = y + z ⇒ x2 + x = x + y + z
⇒ x (x + 1) = x + y + z ⇒ \(\frac{x}{x+y+z}\) = \(\frac{1}{x+1}\)
Similarly, \(\frac{1}{y+1}\) = \(\frac{y}{x+y+z}\) and \(\frac{1}{z+1}\) = \(\frac{z}{x+y+z}\)
∴ \(\frac{1}{x+1}\) + \(\frac{1}{y+1}\) + \(\frac{1}{z+1}\) = \(\frac{x}{x+y+z}\) + \(\frac{y}{x+y+z}\) + \(\frac{z}{x+y+z}\)
= \(\frac{x+y+z}{x+y+z}\) = 1.