Question

if x2+y2=68 and x-y=6 find x3-y3
if u answer this questn then ill post another simple question for 50 marks and ill mark the first answer as brainliest

Answer 1

The answer is in the attachment. Hope it is helpful. :-)...... Second case will be eliminated because if you put the value of x = 4 and y = -2 in x²+y² = 68...... 4²+(-2)² = 68...... 16+4=68........ 20 = 68 which is false so 1st case will only be taken...... so x³-y³=504 is only true.

Answer 2

x² + y² = 68   --- (1)
x - y = 6    --- (2)
(x - y)² = 6²        =>    x² + y² - 2 x y = 36   --- (3)

From (1) and (3),   x y = 16     --- (4)

(x + y)² = x² + y² + 2 x y 
            = 68 + 32 = 100
=> x + y = 10  or  - 10     --- (5)

From  (2) and (5)
  x = 8  and  y = 2       =>  x³ - y³ = 8³ - 2³ = 504  
OR
  x = -2  and y = -8     =>   x³ - y³ = 504
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Another solution:

x² + y² = 68
x - y = 6    =>  x² + y² - 2 x y = 36
=>   x y = (68-36)/2 = 16

x³ - y³ = (x - y) ( x² + xy + y²)
          =  6  *  (68 + 16)
          = 504