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If 5-p = 4-q = 20r, Show that : 1/P + 1/Q + 1/R = 0 - Mathematics

Sum

If 5-P = 4-q = 20r, show that : `1/p + 1/q + 1/r = 0`

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Solution

Let 5-P = 4-q = 20r = k
5-P = k ⇒ 5 = `k^(-1/p)    [ ∵ a^p = b^q ⇒ a = b^(q/p) ]`

4-q = k ⇒ 4 = `k^(-1/q)    [ ∵ a^p = b^q ⇒ a = b^(q/p) ]`

20r = k ⇒ 20 = `k^(1/r)    [ ∵ a^p = b^q ⇒ a = b^(q/p) ]`

5 x 4 = 20
⇒ `k^(-1/p) xx k^(-1/q) = k^(1/r)` 

⇒ `k^( - 1/p- 1/q) = k^(1/r)`

⇒ `k^0 = k^(1/p + 1/q + 1/r)`

If bases are equal, powers are also equal.
⇒  `1/p + 1/q + 1/r = 0`

Concept: Solving Exponential Equations
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (B) | Q 10 | Page 101
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