Respuesta :

VirαtKσhli

Step-by-step explanation:

Here we are given that , the Value of

  • [tex] 3x - 2y = 9 [/tex]
  • [tex] 27x^3 - 8y^3 = 1377 [/tex]

And we need to find the prove that ,

  • [tex] xy = 4 [/tex]

We know a identity as ,

  • [tex] (a-b)^3 = a^3-b^3-3ab(a-b) [/tex]

On cubing both sides of the given equation,

  • [tex] (3x-2y)^3 = 9^3 [/tex]

Simplify and then substitute ,

  • [tex] 27x^3-8y^3 -3(3x)(2y)(3x-2y ) = 729[/tex]

  • [tex] 1377 - 18xy (9) = 729 [/tex]

  • [tex] 162xy = 1377-729 [/tex]

  • [tex] xy =\dfrac{648}{162}[/tex]

  • [tex]xy = 4 [/tex]

Hence Proved !

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