I f 3x-2y7 and xy=-3. Find 27x² -8X²​

Question

I f 3x-2y7 and xy=-3.
Find 27x² -8X²​

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Peyton 1 month 2021-08-20T17:30:24+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-08-20T17:31:39+00:00

    Step-by-step explanation:

    The first equation given,

    x-\frac{1}{x}=5x−

    x

    1

    =5 …….. (i)

    If we do the cube of equation (i) we get,

    \left(x-\frac{1}{x}\right)^{3}=5^{3}(x−

    x

    1

    )

    3

    =5

    3

    x^{3}-\left(\frac{1}{x}\right)^{3}-3 \times x \times\left(\frac{1}{x}\right) \times\left(x-\frac{1}{x}\right)=125x

    3

    −(

    x

    1

    )

    3

    −3×x×(

    x

    1

    )×(x−

    x

    1

    )=125

    x^{3}-\left(\frac{1}{x}\right)^{3}-3\times(x-\frac{1}{x})=125x

    3

    −(

    x

    1

    )

    3

    −3×(x−

    x

    1

    )=125

    x^{3}-\left(\frac{1}{x}\right)^{3}-3 \times 5=125x

    3

    −(

    x

    1

    )

    3

    −3×5=125

    Grouping the terms,

    x^{3}-\left(\frac{1}{x}\right)^{3}=125+15x

    3

    −(

    x

    1

    )

    3

    =125+15

    x^{3}-\left(\frac{1}{x}\right)^{3}=140x

    3

    −(

    x

    1

    )

    3

    =140

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