Question

if x-y=3 and xy=28, find the value of x cube - y cube

Answer 1

${(x - y)}^{2} + 2xy = {x}^{2} + {y}^{2}$

${3}^{2} + 2 \times 28 = {x}^{2} + {y}^{2}$

=65

${x}^{3} - {y}^{3} = (x - y)( {x}^{2} + {y}^{2} + xy )$

=3(65+28)

=279