Question

If 2x
= 4y
= 8z
and xyz = 288 then 1/2x +1/4y +1/8z equals

Answer 1

$\frac{1}{2x} + \frac{1}{4y} + \frac{1}{8z} \\ = \frac{(4y)(8z) + (2x)(8z) + (2x)(4y)}{64xyz} \\ = \frac{(2x)(2x) + (2x)(2x) + (2x)(2x)}{64 \times 288} \\ = \frac{ {4x}^{2} + {4x}^{2} + {4x}^{2} }{18432} \\ = \frac{ {12x}^{2} }{18432} \\ = \frac{ {x}^{2} }{1536}$