Question

Find the value of 64xcube-125zcube if 4x-5z=3/5 and xz=6

Answer 1

Answer:

7.416

Step-by-step explanation:

We can re-write the question as :

Find Value of 64*x^3 - 125*z^3, given that 4x-5z=0.6 and x*z=6

Using identity x^3-y^3=(x-y)(x^2+x*y+y^2)

We know x^2+y^2+x*y=(x-y)^2+2x*y

x^3-y^3=(x-y)((x-y)^2+2*x*y)

(4x)^3-(5z)^3=(4x-5z)((4x-5y)^2+2*4x*5y)

(4x)^3-(5z)^3=0.6*(0.6^2+12)

(4x)^3-(5z)^3=0.6*(0.36+12)

(4x)^3-(5z)^3=0.216+7.2

(4x)^3-(5z)^3=7.416