If a, b and c are three distinct real numbers | vedclass

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(C) Given the limit: $\lim _{x \rightarrow \infty} \frac{(b-c) x^2+(c-a) x+(a-b)}{(a-b) x^2+(b-c) x+(c-a)}=\frac{1}{2}$ Dividing the numerator and den

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$3 b$

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(C) Given the limit: $\lim _{x \rightarrow \infty} \frac{(b-c) x^2+(c-a) x+(a-b)}{(a-b) x^2+(b-c) x+(c-a)}=\frac{1}{2}$ Dividing the numerator and denominator by $x^2$: $\lim _{x}$ ${\rightarrow \infty} \frac{(b-c) + \frac{c-a}{x} + \frac{a-b}{x^2}}{(a-b) + \frac{b-c}{x} + \frac{c-a}{x^2}} = \frac{1}{2}$ As $x \rightarrow \infty$,the terms with $x$ in the denominator approach $0$: $\frac{b-c}{a-b} = \frac{1}{2}$ Cross-multiplying gives: $2(b-c) = a-b$ $2b - 2c = a - b$ $3b = a + 2c$

If $a, b$ and $c$ are three distinct real numbers and $\lim _{x \rightarrow \infty} \frac{(b-c) x^2+(c-a) x+(a-b)}{(a-b) x^2+(b-c) x+(c-a)}=\frac{1}{2}$,then $a+2 c=$

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