Surds and Indices Practice Test 1

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Question : 30 of 40

Marks: +1, -0

Given that

2^x = 3^y = 6^{-z}

, then find the value of

(1/x+1/y+1/z)

.

$- 1/ 2$
$3 /2$
1
0

Solution:

Let

2^x = 3^y = 6^{-z}=k

, then,

k^{1/x} = 2

;

k^{1/y} = 3

;

k^{-1/z} = 6

Now,

2×3=6

⇒k^{1/x}×k^{1/y}=k^{-1/z}

⇒k^{1/x+1 /y} =k^{-1/z}

⇒1/x+1/y=-1/z

∴1/x+1/y+1/z=0

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