Question

Find the value of x³+y³ if x+y = 3 and xy = 2​

Answer 1

Answer:

The Answer is 8

Given, x+y=2

Cube on both sides give,

(x+y)3=x3+y3+3xy(x+y)

(2)3=x3+y3+3xy(2) ………………because, (x+y)=2

Hence,

8=x3+y3+6xy

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Answer 2

x+y = 3

xy=2

(x+y)²−4xy = (3)² − 4(2) = 1 = (x−y)²

∴ x−y = ± 1

Therefore, x = 2, 1

and y = 1, 2

Therefore, x³+y³ = 1+8 =9 =(x+y)²