If x and y are integers such that $x^{2} > y^{2}$ , then $x^{3} > y^{3}$ . State whether the statement is true (T) or false (F).

True

No worries! We‘ve got your back. Try BYJU‘S free classes today!

False

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is B False
Verify the given statement
Let $x = - 2$ and $y = 1$
Then, $x^{2} = {(- 2)}^{2} = 4$
And, $y^{2} = 1$
So, $x^{2} > y^{2}$
Now, $x^{3} = {(- 2)}^{3} = - 8$
And, $y^{3} = 1$
Clearly, $x^{3} < y^{3}$
Hence, the given statement is false.

Suggest Corrections

Similar questions

Question 68

State whether the following statement is true or false:

If x and y are integers such that $x^{2} > y^{2}$ , then $x^{3} > y^{3}$

Question 69

State whether the following statement is true or false:

Let x and y be natural numbers. If x divides y, then $x^{3}$ divides $y^{3}$

Question 45

State whether the statement given is True or False.

Sum of $x^{2} + x$ and $y + y^{2}$ is $2 x^{2} + 2 y^{2}$ .

Question 82

In the following question, state whether the given statements are true (T) or false (F).

$\frac{x^{m}}{y^{m}} = {(\frac{y}{x})}^{- m}$

Question 68

State whether the following statement is true or false:

If x and y are integers such that $x^{2} > y^{2}$ , then $x^{3} > y^{3}$

Join BYJU'S Learning Program