(i) If a(y+z) = b(z+x) = c(x+y) and out of a, b, c no two of them are equal then show that, y - za b - c= z - x b c - a = x - yc a - b(ii) If x3x - y - z = y3y - z - x = z3z - x - y and x + y + z ≠ 0 then show that the value of each ratio is equal to 1.(iii) If ax + byx + y = bx +azx + z = ay + bzy + z and x + y + z ≠ 0 then show that a + b2.(iv) If y + za = z + xb = x + yc then show that xb + c - a = yc + a - b = za + b - c .(v) If 3x - 5y5z + 3y = x + 5zy - 5x = y - zx - z then show that every ratio = xy.

(i) If a(y+z) = b(z+x) = c(x+y) and out of a, b, c no two of them are

1.	(i) If a(y+z) = b(z+x) = c(x+y) and out of a, b, c no two of them are equal then show that, y - za b - c= z - x b c - a = x - yc a - b(ii) If x3x - y - z = y3y - z - x = z3z - x - y and x + y + z ≠ 0 then show that the value of each ratio is equal to 1.(iii) If ax + byx + y = bx +azx + z = ay + bzy + z and x + y + z ≠ 0 then show that a + b2.(iv) If y + za = z + xb = x + yc then show that xb + c - a = yc + a - b = za + b - c .(v) If 3x - 5y5z + 3y = x + 5zy - 5x = y - zx - z then show that every ratio = xy.
Answer» (i) If a(y+z) = b(z+x) = c(x+y) and out of a, b, c no two of them are equal then show that, $\frac{y - z}{a (b - c)} = \frac{z - x}{b (c - a)} = \frac{x - y}{c (a - b)}$ (ii) If $\frac{x}{3 x - y - z} = \frac{y}{3 y - z - x} = \frac{z}{3 z - x - y}$ and $x + y + z \neq 0$ then show that the value of each ratio is equal to 1. (iii) If $\frac{a x + b y}{x + y} = \frac{b x + a z}{x + z} = \frac{a y + b z}{y + z}$ and $x + y + z \neq 0$ then show that $\frac{a + b}{2}$ . (iv) If $\frac{y + z}{a} = \frac{z + x}{b} = \frac{x + y}{c}$ then show that $\frac{x}{b + c - a} = \frac{y}{c + a - b} = \frac{z}{a + b - c}$ . (v) If $\frac{3 x - 5 y}{5 z + 3 y} = \frac{x + 5 z}{y - 5 x} = \frac{y - z}{x - z}$ then show that every ratio = $\frac{x}{y}$ .