Question

If 2^x = 4^y = 8^z and xyz = 288, then `1/(2x) = 1/(4y) + 1/(8z)` equal to

पर्याय

• `11/12`

• `11/96`

• `29/96`

• `27/96`

Answer 1

`11/96`

Explanation:

`2^x = 4^y = 8^z`

⇒ `2^x = 2^(2y) = 2^(3z)`

⇒ `x = 2y = 3z`

⇒ `x : y : z`
    6  : 3 : 2

Now 6A × 3A × 2A = 288  ......[xyz = 288]

⇒ A = 2

∴ `1/(2x) + 1/(4y) + 1/(8z)`

⇒ `1/24 + 1/24 + 1/32 = (4 + 4 + 3)/96`

= `11/96`