The difference between two positive numbers is $4$ and difference of their cubes is $316$ . Find their product.

22

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

20

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

21

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

19

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

Open in App

Solution

The correct option is C $21$
Let, the two number be $x$ and $y$

Therefore,we get $x - y = 4$
$x^{3} - y^{3} = 316$

$x - y = 4$

Squaring both sides,

$=> (x - y)^{2} = 4^{2}$

$=> x^{2} + y^{2} - 2 x y = 16$

$=> x^{2} + y^{2} = 16 + 2 x y$

Now, $x^{3} - y^{3} = 316$

$=> (x - y) (x^{2} + y^{2} + x y) = 316$

$=> 4 (16 + 2 x y + x y) = 316$

$=> 16 + 3 x y = \frac{316}{4}$

$=> 3 x y = 79 - 16$

$=> x y = \frac{63}{3}$

$=> x y = 21$

Suggest Corrections

Similar questions

4

316

4

316

The difference between two numbers is 5 and their products is 14.Find the difference between their cubes.

The difference between two positive numbers x and y is 4 and the difference between their reciprocal is 4÷21. Find the numbers.

Join BYJU'S Learning Program