Question

X/a = y/b=z/c=2018 find xy=(a+b)(b+c)(c+a)/abc(x+y)(y+z)(z+x)

Answer 1

Step-by-step explanation:

Given:

$\frac{x}{a} = \frac{y}{b} = \frac{z}{c} = 2018 \\ \\ \therefore \: \frac{x}{a} = 2018 \implies \: x = 2018 \: a \\ \\ \: \: \: \: \: \frac{y}{b} = 2018 \implies \: y= 2018 \: b \\ \\ \: \: \: \: \: \frac{z}{c} = 2018 \implies \: z = 2018 \: c \\ \\ xy = \frac{(a + b)(b + c)(c + a)}{abc(x + y)(y + z)(z + x)} \\ \\ = \frac{(a + b)(b + c)(c + a)}{abc(2018a+ 2018b)(2018b + 2018c)(2018c + 2018a)} \\ \\ = \frac{(a + b)(b + c)(c + a)}{abc \times 2018(a+ b) \times 2018(b + c) \times 2018(c + a)} \\ \\ = \frac{(a + b)(b + c)(c + a)}{abc \times (2018)^{3} (a+ b)(b + c)(c + a)} \\ \\= \frac{1}{abc \times (2018)^{3} } \\ \\thus \\ \boxed{ xy = \frac{1}{abc \times (2018)^{3} } }$