Question

If x/ y + y/x=1(x,y is not equal to 0) , find the value of x^3 + y^3

Answer 1

0

Step-by-step explanation:

Given:

$\dfrac{x}{y} + \dfrac{y}{x} = 1$

To find:

The value of x³ + y³

How to solve:

1. Solve the given first till a accurate value.

2. Use Algebra Formula.

3. Substitute the given value.

4. Simplify and get answer.

Solution:

$\dfrac{x}{y} + \dfrac{y}{x} = 1 \\ \\ [\textsf{By Taking L.C.M}] \\ \\ \frac{ {x}^{2} + {y}^{2} }{xy} = 1 \\ \\ [\textsf{By Cross Multiply}]\\ \\ {x}^{2} + {y}^{2} = xy \\ \\ {x}^{2} - xy + {y}^{2} = 0 -- - - (1)$

Now,

${x}^{3} + {y}^{3} \\ \\ = (x + y)( {x}^{2} - xy + {y}^{2}) \\ \\ = (x + y) \times 0 [\textsf{From 1}]\\ \\ = 0$

Therefore, The required answer is 0.

Algebra Formula Used

x³ + y³ = (x + y)(x²- xy + y²)

Answer 2

Answer:

Hence your answer is 0

Step-by-step explanation:

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