Question

solve the above problem ​

Answer 1

$\dfrac{76}{49}$

Step-by-step explanation:

Given:

$\dfrac{ {x}^{2} + {y}^{2} }{ {x}^{2} - {y}^{2} } = 2 \dfrac{1}{8}$

To find:

$\dfrac{ {x}^{3} + {y}^{3} }{ {x}^{3} - {y}^{3} }$

How to Solve?

Basically, I we simplify given we will get the value of x/y then Try to solve To find by the help of formula and put the value you get before,

Solution:

$\frac{ {x}^{2} + {y}^{2} }{ {x}^{2} - {y}^{2} } = 2 \frac{1}{8} \\ \\\frac{ {x}^{2} + {y}^{2} }{ {x}^{2} - {y}^{2} } = \frac{17}{8} \\ \\ \sf [Applying \: componendo\: and\: dividendo]\\ \\ \frac{ {x + y}^{2} + {x}^{2} - {y}^{2} }{ {x}^{2} + {y}^{2} - {x}^{2} + {y}^{2} } = \frac{17 + 8}{17 - 8} \\ \\ \frac{2 {x}^{2} }{2 {y}^{2} } = \frac{25}{9} \\ \\ \frac{ {x}^{2} }{ {y}^{2} } = \frac{25}{9} \\ \\ \frac{x}{y} = \frac{5}{3} \implies \: x = \frac{5y}{3}$

Now,

See in the attachment,

Formula Used

Componendo and Dividendo

$\frac{a}{b} = \frac{c}{d} \implies \frac{a+b}{a-b} = \frac{c+d}{c-d} \\ \\ a³ + b³ = (a+b)³ - 3ab(a+b) \\ \\ a³ - b³ = (a-b)³ + 3ab(a-b)$

Answer 2

Answer:

\dfrac{76}{49}

49

76

Step-by-step explanation:

Given:

\dfrac{ {x}^{2} + {y}^{2} }{ {x}^{2} - {y}^{2} } = 2 \dfrac{1}{8}

x

2

−y

2

x

2

+y

2

=2

8

1

To find:

\dfrac{ {x}^{3} + {y}^{3} }{ {x}^{3} - {y}^{3} }

x

3

−y

3

x

3

+y

3

How to Solve?

Basically, I we simplify given we will get the value of x/y then Try to solve To find by the help of formula and put the value you get before,

Solution:

\begin{gathered} \frac{ {x}^{2} + {y}^{2} }{ {x}^{2} - {y}^{2} } = 2 \frac{1}{8} \\ \\\frac{ {x}^{2} + {y}^{2} }{ {x}^{2} - {y}^{2} } = \frac{17}{8} \\ \\ \sf [Applying \: componendo\: and\: dividendo]\\ \\ \frac{ {x + y}^{2} + {x}^{2} - {y}^{2} }{ {x}^{2} + {y}^{2} - {x}^{2} + {y}^{2} } = \frac{17 + 8}{17 - 8} \\ \\ \frac{2 {x}^{2} }{2 {y}^{2} } = \frac{25}{9} \\ \\ \frac{ {x}^{2} }{ {y}^{2} } = \frac{25}{9} \\ \\ \frac{x}{y} = \frac{5}{3} \implies \: x = \frac{5y}{3} \end{gathered}

x

2

−y

2

x

2

+y

2

=2

8

1

x

2

−y

2

x

2

+y

2

=

8

17

[Applyingcomponendoanddividendo]

x

2

+y

2

−x

2

+y

2

x+y

2

+x

2

−y

2

=

17−8

17+8

2y

2

2x

2

=

9

25

y

2

x

2

=

9

25

y

x

=

3

5

⟹x=

3

5y

Now,

See in the attachment,

Formula Used

Componendo and Dividendo

\begin{gathered} \frac{a}{b} = \frac{c}{d} \implies \frac{a+b}{a-b} = \frac{c+d}{c-d} \\ \\ a³ + b³ = (a+b)³ - 3ab(a+b) \\ \\ a³ - b³ = (a-b)³ + 3ab(a-b) \end{gathered}

b

a

=

d

c

⟹

a−ba+b =c−dc+da³+b³=(a+b)³−3ab(a+b)a³−b³=(a−b)³+3ab(a−b)