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If $x + \sqrt{5} = 5 + \sqrt{y}$ $x + \sqrt 5 = 5 + \sqrt y$ and x, y are positive integers, then the value of $\frac{\sqrt{x} + y}{x + \sqrt{y}}$ $\frac{{\sqrt x + y}}{{x + \sqrt y }}$ is?

Answer:- 1

Explanation:-

Solution:

\begin{aligned} x + \sqrt{5} = 5 + \sqrt{y} \\ Put , x = 5 and y = 5 \\ 5 + \sqrt{5} = 5 + \sqrt{5} \\ L .H .S = R .H .S \\ \frac{\sqrt{x} + y}{x + \sqrt{y}} \\ = \frac{\sqrt{5} + 5}{5 + \sqrt{5}} \\ = 1 \end{aligned}

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and x, y are positive integers, then the value of

\frac{\sqrt{x} + y}{x + \sqrt{y}}

$\frac{{\sqrt x + y}}{{x + \sqrt y }}$ is?", "text": "If

x + \sqrt{5} = 5 + \sqrt{y}

$x + \sqrt 5 = 5 + \sqrt y$ and x, y are positive integers, then the value of

\frac{\sqrt{x} + y}{x + \sqrt{y}}

$\frac{{\sqrt x + y}}{{x + \sqrt y }}$ is?", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} x + \sqrt{5} = 5 + \sqrt{y} \\ Put , x = 5 and y = 5 \\ 5 + \sqrt{5} = 5 + \sqrt{5} \\ L .H .S = R .H .S \\ \frac{\sqrt{x} + y}{x + \sqrt{y}} \\ = \frac{\sqrt{5} + 5}{5 + \sqrt{5}} \\ = 1 \end{aligned}

$\eqalign{ & x + \sqrt 5 = 5 + \sqrt y \cr & {\text{Put , }}x = 5{\text{ and }}y = 5 \cr & 5 + \sqrt 5 = 5 + \sqrt 5 \cr & {\text{L}}{\text{.H}}{\text{.S}} = {\text{R}}{\text{.H}}{\text{.S}} \cr & \frac{{\sqrt x + y}}{{x + \sqrt y }} \cr & = \frac{{\sqrt 5 + 5}}{{5 + \sqrt 5 }} \cr & = 1 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution: