If 5^x = 3^y =45^z, prove that
1/z = 1/x + 2/y
Please answer....
Answers
Answered by
11
Answer:
1 / z = 2/y + 1/x
Explanation:
let 5^x = 3^y = 45^z = k
5^x = k ⇒ 5 = k^(1/x)
3^y = k ⇒ 3 = k^(1/y)
45^z = k ⇒ 45 = k^(1/z)
⇒ 45 = 3 * 3 * 5
⇒ 45 = 3^2 * 5
⇒ k^(1/z) = [ k^(1/y) ]^2 * k^(1/x)
⇒ k^(1/z) = k^(2/y) * k^(1/x)
⇒ k^(1/z) = k^( 2/y + 1/x )
⇒ 1/z = 2/y + 1/x
Proved.
Answered by
27
•5^x=3^y=45^z
By squaring 45^z ,
(45^z)^2 = (5^x)×(35^y)
Expanding 45,
5×9=45
=(5×3^2)^2z = (5^x)×(35^y)
=5^2z×3^4z = (5^x)×(35^y)
Hence,
2z =x and 4z = y
1/x = 1/2z,
1/y = 1/4z
Hence,
1/x + 2/y = 1/2z + 1/2z = 1/z
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