Question

please help with this question

Answer 1

Given:-

☆Value of 4x-5z=16

☆Value of xz=12

To find:-

☆Value of 64x³-125z³

Solution:-

By cubing both sides in the equation,4x-5z=16,we get:-

=>(4x-5z)³=(16)³

We know that,(a-b)³=a³-b³-3ab(a-b)

=>(4x)³-(5z)³-3×4x×5z(4x-5z)=4096

=>64x³-125z³-60xz(16)=4096

=>64x³-125z³-60×12×16=4096

=>64x³-125z³-11520=4096

=>64x³-125z³=4096+11520

=>64x³-125z³=15616

Thus,value of 64x³-125z³ is 15616.

Extra Information:-

☆Some of the important algebraic identities used in this type of problems are:-

•(a+b)²=a²+b²+2ab

•(a-b)²=a²+b²-2ab

•a²-b²=(a+b)(a-b)

•(a+b)³=a³+b³+3ab(a+b)

•(a-b)³=a³-b³-3ab(a-b)

•a³+b³=(a+b)(a²+b²-ab)

•a³-b³=(a-b)(a²+b²+ab)

Answer 2

Answer:

Given - 4x - 5z = 16

- xy = 12

To find -

4x - 5z = 16

(4x- 5z)^2 = 16^2

16x^2 + 25z^2 - 40xy = 256

16x^2 + 25z ^2 - 40 × 12 = 256

16x^2 + 25z^2 - 480 = 256

16x^2 + 25z^2 = 256+ 480

16x^2 + 25z^2 = 736

4( 4x^2 + 5z^2)= 756

4x^2 + 5z^2 = 756 × 4

4x^2 + 5z^2 = 3024

64x^3 - 125z^3

( 4x)^3 - (5z)^3

using identity a^3 - b^3 = (a - b)(a^2 + ab + b^2).

( 4x - 5z) ( 4x^2 + 4x × 5z + 5z^2)

( 16 ) ( 4x^2 + 5z^2 + 20xy)

(16) ( 3024 + 20× 12)

16 ( 3024 + 240)

16 ( 32 64)

52,224