Question

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

Answer 1

Answer:

25°15'35.7"N 86°59'21.9

Answer 2

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1st Equation,

$x + y = 3 \\ \implies x = 3 - y$

2nd Equation,

$xy = 2 \\ \implies x \times y = 2 \\ x = \frac{y}{2}$

From 1st Equation and 2nd Equation,

$\implies x = 3 - y$

$\implies \frac{y}{2} = 3 - y \\ \implies y = 2(3 - y) \\ \implies y = 6 - 2y \\ \implies y + 2y = 6 \\ \implies 3y = 6 \\ \implies y = \frac{6}{3} \\ \implies y = \frac{ \cancel{6}}{ \cancel{3}} \\ \implies y = 2$

Now , We can find value of x from Equation 1 or Equation 2

I am taking Equation 1

From Equation 1 ,

$\implies x = 3 - y \\ \implies x = 3 - 2 \\ \implies x = 1$

Now We will find X³ + Y³

$\implies {x}^{3} + {y}^{3} \\ \implies {1}^{3} + {2}^{3} \\ \implies 1 \times 1 \times 1 + 2 \times 2 \times 2 \\ \implies 1 \times 1 + 2 \times 2 \\ \implies 1 + 4 \\ \implies 5$

Hence ,

X³ + Y³ = 5

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