If the left-hand side of the equation is a perfect square

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

If the left-hand side of the equation a(b−c)x2+b(c−a)xy+c(a−b)y2=0a(b-c)x^2+b(c-a)xy+c(a-b)y^2=0 is a perfect square, find the value of {log⁡(a+c)+log⁡(a−2b+c)log⁡(a−c)}2,\left\{\frac{\log(a+c)+\log(a-2b+c)}{\log(a-c)}\right\}^2, where a,b,c∈R+a,b,c\in\mathbb{R}^+ and a>ca>c.

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