Question

if p^1/x =q^1/y=r^1/z and pqr=1, then prove that x+y+z=0​

Answer 1

Step-by-step explanation:

Here's your answer.

Hope, it helps.

please follow me.

Answer 2

Question :- if p^(1/x) = q^(1/y) = r^(1/z) , and pqr = 1 , prove that, x + y + z = 0 .

Solution :-

Let us assume that,

→ p^(1/x) = q^(1/y) = r^(1/z) = k , (where k is a constant number.)

then,

→ p^(1/x) = k

→ p = k^x

similarly,

→ q^(1/y) = k

→ q = k^y

and,

→ r^(1/z) = k

→ r = k^z .

given that,

→ p * q * r = 1 .

putting above values we get,

→ k^x * k^y * k^z = 1

using a^l * a^m * a^n = a^(l + m + n) , we get,

→ k^(x + y + z) = 1

now, we know that, if power of a number is 0 , it is equal to 1,

therefore,

→ k^(x + y + z) = k^0

now, we know that, when base is same, powers are equal . { a^m = a^n => m = n }

hence,

→ (x + y + z) = 0 (Proved.)

Learn more :-

if the positive square root of (√190 +√ 80) i multiplied by (√2-1) and the

product is raised to the power of four the re...

https://brainly.in/question/26618255