If 5^x = 30^{-y} = 6^z , then what isthe value of (xy + yz + zx) / {xyz} ?

SSC CGL 11 Aug 2017 Shift 1 Paper

Question : 64 of 100

Marks: +1, -0

5^x = 30^{-y} = 6^z

, then what isthe value of

(xy + yz + zx) / {xyz}

Solution:

5^x = 30^{-y} = 6^z

5-(k)^{1/x},30=(k)^{1/{-y}},6=(k)^{1/z}

5× 6=3 0

⇒

(k)^{1/x}× (k)^{1/z}=(k)^{1/{-y}}

⇒

(k)^{1/x+1/z}=(k)^{-1/{y } }

∵ Base are equal, on comparing power
⇒

1/x+1/z=-1/y

⇒

1/x+1/y+1/z=0

∴

{xy + yz + zx}/{xyz}=0

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