Question

If x+y-1=0 then prove that x cube + y cube +3xy =1

Answer 1

x+y=1

x³+y³= (x+y) (x² + y² -xy)

x³+y³= (x+y) ( (x+y)² - 2xy -xy)

x³+y³= (x+y) ( (x+y)² - 3xy)

Now put x+y=1

x³+y³= (1) ( (1)² - 3xy)
x³+y³= 1- 3xy
x³ + y³ + 3xy = 1

Hence proved!

I hope you understand the approach.

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Answer 2

Answer:

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