Question

If x-y = 2 and xy=3, find x³ - y³

Answer 1

Answer:

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

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

$(2)( {x - y})^{2} + 3 \times 3$

$(2)( {2}^{2} + 9)$

$2 \times 4 + 9$

$2×13$

=26

Answer 2

Answer: 26

Step-by-step explanation:

x-y=2,xy=3

so x+y = root over of (x-y)²+4xy

= root over of 2²+3×4

=root over of 16

=4

x+y=4

then

x³-y³=(x-y)(x²+xy+y²)

=2[(x²+2xy+y²)-xy]

= 2[(x+y)²-xy]

=2[4²-3]

= 2×13=26

so the ans is 26

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