Question 72

$$\frac{(a-b)^{2}}{(b-c) (c-a)}+\frac{(b-c)^{2}}{(a-b) (c-a)}+\frac{(a-c)^{2}}{(a-b) (b-c)}$$, $$a\neq b\neq c$$ is

Solution

Let a=3, b=2, c=1

$$\frac{(a-b)^{2}}{(b-c) (c-a)}+\frac{(b-c)^{2}}{(a-b) (c-a)}+\frac{(a-c)^{2}}{(a-b) (b-c)}$$

= $$\frac{(3-2)^{2}}{(2-1) (1-3)}+\frac{(2-1)^{2}}{(3-2) (1-3)}+\frac{(3-1)^{2}}{(3-2) (2-1)}$$

= -$$\frac{1}{2}-\frac{1}{2}$$+4=3

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