CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

nth Term of A.P

If 3x-4y=5 ...

Question

If $3 x - 4 y = 5$ and $x y = 3$ , then find $27 x^{3} - 64 y^{3}$ .

A

125

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

B

665

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

C

225

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

D

985

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

Open in App

Solution

The correct option is B 665
$3 x - 4 y = 5$
Cubing both sides,
$(3 x - 4 y)^{3} = 5^{3}$

Applying the formula, ${(a - b)}^{3} = a^{3} - b^{3} - 3 a b (a - b)$
$(3 x)^{3} - (4 y)^{3} - 3 \times 3 x \times 4 y \times (3 x - 4 y)) = 125$
$(3 x)^{3} - (4 y)^{3} - 36 \times x y \times (3 x - 4 y) = 125$
Substituting, $3 x - 4 y = 5; x y = 3$

$27 x^{3} - 64 y^{3} - 36 \times 3 \times 5 = 125$
$27 x^{3} - 64 y^{3} = 125 + 540 = 665$

Suggest Corrections

thumbs-up

0

Similar questions

5 x - 4 y = 7

x y = 8

125 x^{3} - 64 y^{3}

3 x + 2 y = 9

x y = 3

27 x^{3} + 8 y^{3}

3 x - 2 y = 13

x y = 5

, find the value of

27 x^{3} - 8 y^{3}

3 x - 2 y = 11

x y = 12

, find the value of

27 x^{3} - 8 y^{3}

3 x + \frac{1}{3 x} = 3

27 x^{3} + \frac{1}{27 x^{3}}

.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Arithmetic Progression

MATHEMATICS

Watch in App

explore_more_icon

Explore more

nth Term of A.P

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon