Question

if x+y=10 and xy=3 then x3-y3/x2-y2 =?

Answer 1

Hello friend
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x³- y³= (x - y) ( x² + y² +xy )= (x - y) (x² + y² + 2xy - xy )
Since ( x + y ) = x² +y² + 2xy
x³ - y³ = ( x - y ) [ ( x + y )² - xy ]
Also,
x² - y² = ( x - y ) ( x + y )
Now
( x³-y³) / ( x²-y²)= (x - y) [(x + y)² - xy] / [ (x - y) (x + y) ]= [ (x + y)² - xy ] /(x +y)
Now given, x + y = 10 and xy = 3. Putting these values in above equation we get,
(x³ - y³) / (x² -y²) = [(x+y)²-xy ] / (x+y) = (10²-3) /10 = (100-3) / 10 = 97/10=9.7
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Hope it helped u