Question

Prove x+y+z=0
Please Solve Guys.....​

Answer 1

Step-by-step explanation:

Given---> p¹/ˣ = p¹/ʸ = p¹/ᶻ and pqr = 1

To prove---> x + y + z = 0

Proof ---> ATQ,

p¹/ˣ = p¹/ʸ = p¹/ᶻ = k ( say )

Now,

p¹/ˣ = k

=> { ( p )¹/ˣ }ˣ = kˣ

=> p = kˣ

Similarly , p = kʸ , p = kᶻ

ATQ, pqr = 1

Putting value of p , q and r , we get,

=> kˣ kʸ kᶻ = 1

We have a law of exponent , aˡ aᵐ aⁿ = aˡ⁺ᵐ⁺ⁿ , applying it here , we get,

=> kˣ⁺ʸ⁺ᶻ = 1

We know that, k⁰ = 1 , putting it here we get,

=> kˣ⁺ʸ⁺ᶻ = k⁰

Comparing exponent we get,

=> x + y + z = 0

Additional information--->

1) aᵐ aⁿ = aᵐ⁺ⁿ

2) aᵐ ÷ aⁿ = aᵐ⁻ⁿ

3) ( aᵐ )ⁿ = aᵐⁿ

4) a⁰ = 1

5) 1 / aᵐ = a⁻ᵐ

6) ( ab )ᵐ = aᵐ bᵐ