Math, asked by rumasinha529, 11 months ago

if x is equal to 1 Y is equal to minus 2 and Z is equal to 3 find the value of x cube+y cube+z cube-3xyz​

Answers

Answered by abhishesumesh
5

Step-by-step explanation:

Answer:

x ^ { 3 } + y ^ { 3 } + z ^ { 3 } = 3 x y zx

3

+y

3

+z

3

=3xyz

Hence proved

Solution:

Given that

x+y+z=0x+y+z=0

x ^ { 3 } + y ^ { 3 } + z ^ { 3 } = 3 x y zx

3

+y

3

+z

3

=3xyz

The above expression can be written as like

x ^ { 3 } + y ^ { 3 } + z ^ { 3 } - 3 x y z = ( x + y + z ) \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - x y - y z - z x \right)x

3

+y

3

+z

3

−3xyz=(x+y+z)(x

2

+y

2

+z

2

−xy−yz−zx)

Substitute the given value x+y+z=0x+y+z=0 in the above equation

Therefore we will get,

x ^ { 3 } + y ^ { 3 } + z ^ { 3 } - 3 x y z = 0 \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - x y - y z - z x \right)x

3

+y

3

+z

3

−3xyz=0(x

2

+y

2

+z

2

−xy−yz−zx)

If any value is multiplied with zero than total value will be equal to zero

\begin{lgathered}\begin{array} { l } { x ^ { 3 } + y ^ { 3 } + z ^ { 3 } - 3 x y z = 0 } \\\\ { x ^ { 3 } + y ^ { 3 } + z ^ { 3 } = 3 x y z } \end{array}\end{lgathered}

x

3

+y

3

+z

3

−3xyz=0

x

3

+y

3

+z

3

=3xyz

please mark me as brainliest ⭐

Hence proved.

Similar questions