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If 2x+3y=12 and xy=6 find 8x*x*x …

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If 2x+3y=12 and xy=6 find 8x*x*x + 27*y*y*y
  • 1 answers

Dharmendra Kumar 7 years, 10 months ago

8x3+27y3=23x3+33y3=(2x)3+(3y)3       [by using anbn=(ab)n]

Now by using identity 

(a+b)3=a3+b3+3ab(a+b)

a3+b3=(a+b)3 - 3ab(a+b)       ---------(1)

Now 8x3+27y3=(2x)3+(3y)3

                          = (2x+3y)3-3(2x)(3y)(2x+3y)      [by using equation (1) put a=2x  and b=3y]

                          =  (2x+3y)3 - 18xy(2x+3y)

                          = (12)3  - 18×6×12                     [given 2x+3y =12   and    xy= 6]

                          =1728 -1296

                          = 432

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