Question

If 3x - 2y = 9 , 27x³- 8y³= 1377 , prove that xy = 4

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Answer 1

Explanation:

Here we are given that , the Value of

• 
  `3x - 2y = 9`
• 
  `27x^3 - 8y^3 = 1377`

And we need to find the prove that ,

• 
  `xy = 4`

We know a identity as ,

• 
  `(a-b)^3 = a^3-b^3-3ab(a-b)`

On cubing both sides of the given equation,

• 
  `(3x-2y)^3 = 9^3`

Simplify and then substitute ,

• 
  `27x^3-8y^3 -3(3x)(2y)(3x-2y ) = 729`

• 
  `1377 - 18xy (9) = 729`

• 
  `162xy = 1377-729`

• 
  `xy =(648)/(162)`

• 
  `xy = 4`

Hence Proved !