Question

# If where a<1, b<1 then

- xy+xz=yz+x
- xyz=x+y+z
- xy+yz=xz+y
- yz+zx=xy+z

Hint:

**We can write x as**

**Similarly, we can write y as**

**Similarly, we can write z as**

Multiply ab and equate the values and simplify

## The correct answer is: yz+zx=xy+z

### Given : , where a<1, b<1

To find : A relationship between x, y and z

We can write x as

Similarly, we can write y as

Similarly, we can write z as

Solving the above, we get

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Here note that the fifth term is having fourth power of 2 and not fifth power. We need not to find all nine terms separately; only finding the product is enough because that product will then be written in the form of the term that is known. Terms in a G.P. are having a common ratio in between. That’s why the power of r is increasing as the terms are increasing.