Question

find the solution:
If x= -1/2 & y=1/3
​

Answer 1

Answer:

As (x+y)^3 = x^3 + y^3 + 3*x*x*y + 3*x*y*y

As x+y = -1/3 so (x+y)^3 = -1/27

-1/27 = x^3 + y^3 + 3*x*x*y + 3*x*y*y

x^3 + y^3 + 1/27 = -3*x*x*y - 3*x*y*y

Subtracting x*y from both sides

x^3 + y^3 + 1/27 - x*y = -3*x*x*y - 3*x*y*y - x*y

x^3 + y^3 + 1/27 - x*y = -x*y*(3*x + 3*y + 1)

x^3 + y^3 + 1/27 - x*y = -x*y[3(x + y) +1]

x^3 + y^3 + 1/27 - x*y = -x*y[3*(-1/3) + 1]

x^3 + y^3 + 1/27 - x*y = -x*y[(-1) + 1]

x^3 + y^3 + 1/27 - x*y = -x*y[0]

x^3 + y^3 + 1/27 - x*y = 0

Answer 2

Answer:

$(x + y)(x - y) = {x}^{2} - {y}^{2} \\ \\ ( - \frac{1}{2} + \frac{1}{3} )( - \frac{1}{2} - \frac{1}{3} ) \\ \\ { (\frac{ - 1}{2}) }^{2} - ( { \frac{1}{3}) }^{2} \\ \\ \frac{1}{4} - \frac{1}{9} \\ \\ \frac{9 - 4}{36} \\ \\ \frac{5}{36}$

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