Question 20

If (x + y) = 3, xy = 2, then what is the value of $$x^3+y^3$$:

Solution

Given,

x + y = 3 and xy = 2

$$x^3+y^3\ =\ \left(x+y\right)\left(x^2+y^2-xy\right)$$

x + y = 3

squaring on both sides

$$\left(x+y\right)^2$$ = 9

$$x^2+y^2+2xy$$ = 9

$$x^2+y^2$$ = 9-4 = 5

$$x^3+y^3$$ = 3(5-2) = 9

Answer is option D.

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