If x/y+ y/x = 1 and x + y = 2, then the value of x³ + y³ is :

If x/y+ y/x = 1 and x + y = 2, then the value of x³ + y³…

If $\frac x y+ \frac y x = 1$ and x + y = 2, then the value of x³ + y³ is :

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Correct answer: C

Explanation

The correct answer is Option 3 i.e. 0.

We know that,

x³ + y³ = (x + y)(x² - xy + y²).....(1)

⇒ $\frac x y+ \frac y x = 1$

⇒ $\frac {x^2+y^2} {xy}= 1$

⇒ ${x^2+y^2} = xy$

⇒ ${x^2+y^2} - xy = 0$ ......(2)

Putting eq 2 in 1

⇒ x³ + y³ = (x + y)(0)

⇒ x³ + y³ = 0