Math, asked by letstakeaselfie2035, 10 hours ago

if 2x-5y= 7z-3y then ,for xyz is not equal to zero , find(8 x^3 -343y^3 -8z^3)/(xyz)=

Answers

Answered by yaminiyerra100
0

Answer:

let's start with the assumption that

y=1 and z=1

so putting them in the given equation of

2x-5y= 7z-3y2x−5y=7z−3y

we get

2x-5(1)= 7(1)-3(1)2x−5(1)=7(1)−3(1)

from this we get

2x-5= 7-32x−5=7−3

2x-5= 42x−5=4

2x= 4+52x=4+5

2x= 92x=9

dividing by 2 we get the value of x as

x=4.5x=4.5

so we got the values of x, y, and z as

\begin{gathered}x=4.5\\ y=1\\z=1\end{gathered}

x=4.5

y=1

z=1

putting them in the given question we get

\frac{x^3-y^3-z^3}{xyz}=\frac{(4.5)^3-1^3-1^3}{4.5\times 1 \times 1}

xyz

x

3

−y

3

−z

3

=

4.5×1×1

(4.5)

3

−1

3

−1

3

solving the right hand side we get

\frac{x^3-y^3-z^3}{xyz}=\frac{91.125-1-1}{4.5}

xyz

x

3

−y

3

−z

3

=

4.5

91.125−1−1

\frac{x^3-y^3-z^3}{xyz}=\frac{91.125-2}{4.5}

xyz

x

3

−y

3

−z

3

=

4.5

91.125−2

\frac{x^3-y^3-z^3}{xyz}=\frac{89.125}{4.5}

xyz

x

3

−y

3

−z

3

=

4.5

89.125

hence we get the answer as

\bf{\frac{x^3-y^3-z^3}{xyz}=19.8}

xyz

x

3

−y

3

−z

3

=19.8

This of course a non trivial solution as we had three variables and one equation.

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