Question

XY=3 YZ=9 ZX=27 THEN FIND 2X +2Y+ 2Z=​

Answer 1

$xy = 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: (i) \\ yz = 9 \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: (ii) \\zx = 27 \: \: \: \: \: \: \: \: \: \: \: \: ... \: (iii) \\ \\ dividing \: (ii) \: by \: (i) \\ \\ \frac{yz}{xy} = \frac{9}{3} \\ \frac{z}{x} = 3 \\ z = 3x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: (iv) \\ \\ subtituting \: in \: (iii) \\ \\ (3x)x = 27 \: \: \: \: \: = > \: 3 {x}^{2} = 27 \\ {x}^{2} = \frac{27}{3} = 9$

$x = ± 3$ ... (a)

$substituting \: in \: (iv)$

$z = 3(±3)$

$z = ± 9$ ... (b)

$substituting \: in \: (ii)$

$y(± 9) = 9$

$y = ± 1$ ... (c)

hence,

2x + 2y + 2z

= 2(±3) + 2(±1) + 2(±9) ... (from a, b, c)

= ±6 ± 2 ± 18

= ±(6 + 2 + 18)

= ±26

Hence, here, 2x + 2y + 2z = ±26.