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Special Type of Equations:

(i) Square Cases:

Now in this case we can see that both the equations have one negative and another positive value.

Now,

Now we can see that the answer will be relationships between x and y can not be determined.

Note: Whenever both the equations are given in the square form, our answer will be CAN NOT BE DETERMINED.

(ii) One equation in the square form and another is in square root form:

Now,

So, we can say that the relation between x and y can not be established.

(iii) When both the equations have cubes:

Note:

(iv) When one equation is in square form and another equation is in cube form:

Now,

So, we can say that x ≤ y.

Now,

So, we can say that the relationships can not be determined.

Example 1:

Solution:

Now, 

Clearly say that, x > y             

Answer:  Option (B)

Example 2:

Solution:

 Now, 

So, we can clearly say that the relationships can not be established. 

Answer:  Option (E)

Example 3:

Solution:

Now,

We can say that x > y.

Answer:  Option (A)

Example 4:

Solution:

Now,

So, we can clearly say that the relationships between x and y can not be established. 

Answer:  Option (E)

Example 5:

Solution:

Now,

So, we can clearly say that the relationships between x and y can not be established. 

Answer:  Option (E)