Question

$\Huge\fbox{\color{red}{Questions}}$​

$\sf \: if \: \frac{ {x}^{2} + {y}^{2} }{ {x}^{2} - {y}^{2} } = \frac{17}{8} \: then \: the \: value \: x:y \: \: is$
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Answer 1

Step-by-step explanation:

$\frac{ {x}^{2} + {y}^{2} }{ {x}^{2} - {y}^{2} } = \frac{17}{8} \\ \\ = > \frac{ {x}^{2} + {y}^{2} + {x}^{2} - {y}^{2} }{ {x}^{2} + {y}^{2} - ( {x}^{2} - {y}^{2} ) } = \frac{17 + 8}{17 - 8} \\ \\ = > \frac{ {x}^{2} + {y}^{2} + {x}^{2} - {y}^{2} }{ {x}^{2} + {y}^{2} - {x}^{2} + {y}^{2} } = \frac{25}{9} \\ \\ = > \frac{2 {x}^{2} }{2 {y}^{2} } = \frac{25}{9} \\ \\ = > \frac{ {x}^{2} }{ {y}^{2} } = \frac{25}{9} \\ \\ = > \frac{x}{y} = \sqrt{ \frac{25}{9} } \\ \\ = > \frac{x}{y} = \frac{5}{3}$

x/y = 5/3

=> x : y = 5 : 3

Answer 2

★ $\rm{Answer}$

➼ 5 : 4 is the answer!!

★Given

$=> \sf \: \frac{ {x}^{2} + {y}^{2} }{ {x}^{2} - {y}^{2} } = \frac{17}{8}$

On applying componendo and dividendo, we get

$\sf \: ⇒\frac{ {x}^{2} + {y}^{2} }{ {x}^{2} - {y}^{2} } = \frac{17}{8}$

$\sf = > \frac{( {x}^{2} + {y}^{2})( {x}^{2} - {y}^{2} ) }{ ({x}^{2} + {y}^{2} ) - ( {x}^{2} - {y}^{2}) } = \frac{17 + 8}{17 - 8}$

$\sf \: : \: = > \frac{2 {x}^{2} }{2 {y}^{2} } = \frac{25}{9}$

$\sf : = > \frac{ {x}^{2} }{ {y}^{2} } = {\frac{5}{3} }^{2}$

On taking square root both sides, we get

$= \frac{x}{y} = \frac{5}{3}$

$\text{⇒ ∴ x : y = 5 : 3}$

The answer is 5 : 3

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What is algebric expression?

In mathematics, an algebraic expression is an expression made up from integer constants, variables, and the algebraic operations, addition, subtraction, multiplication, division etc

EXAMPLE = $\sf {x}^{2}$