Discussion

Question:

If $\frac{p a}{b + c} = \frac{p b}{c + a} = \frac{p c}{a + b}$ = 𝓁, then what is the value of ‘𝓁’ if p ≠ 0, a + b + c ≠ 0

Explanation:

pa/(b + c) = pb/(c + a) = pc/(a + b) = 𝓁

⇒ pa/(b + c) = 𝓁; pb/(c + a) = 𝓁; pc/(a + b) = 𝓁

So, pa = b𝓁 + c𝓁,

pb = c𝓁+a𝓁,

pc = a𝓁 + b𝓁

Now adding these 3 equations, p(a + b + c) = 𝓁(b + c + c +a + a + b)

⇒ p(a + b + c) = 2𝓁(a + b + c)

As a + b + c ≠ 0,

p = 2𝓁

∴ 𝓁 = p/2

Hence, option (c).

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