Question

If 3 X + Y + Z is equal to zero show that 27 x cube + b cube + Z cube is equal to 9 x y z






if 3 X + Y + Z equal to zero show that 27 x cube + y cube + Z cube equal to 9 x y z

Answer 1

Step-by-step explanation:

Given 3X + Y + Z = 0

And also given to show that 27 cube + y cube + z cube = 9xyz

LHS RHS

3X + Y + Z = 0

Y+Z = 0 -3X

Y + Z = -3X

As they said to show another equation in cubes we do cubing in equation

That is

LHS RHS

(Y+Z)cube = (-3X) cube

LHS= (Y+ Z) square x (Y+Z)

= Y cube + 2Y square Z + YZ square + Y square Z + 2YZ square + Z cube

Grouping like terms

Y cube + (2Y square Z + Y square Z) + (YZ square + 2YZ square) + Z cube

= Y cube + 3Y square Z + 3YZ square + Z cube

= Y cube + 3YZ(Y+Z) + Z cube

Now Y + Z = -3X

Substitute

Y cube + 3YZ(-3X)+Z cube

= Y cube -9XYZ + Z cube

RHS= -3X cube

= -27X cube

Now equate

LHS RHS.

Y cube -9XYZ + Z cube = -27X cube

Y cube + 27X cube + Z cube = -9XYZ

Hence proved

Y cube + 27X cube + Z cube = -9XYZ