Test Index

Algebra and Applications Test 3

© examsnet.com

Question : 17 of 25

Marks: +1, -0

if

2x = \sqrt{5} + \frac{1}{\sqrt{5}}

, then the value of

\frac{\sqrt{x^{2}-1}}{x-\sqrt{x^{2}-1}}

is ____.

2
1
3
5

Solution:

Concept:

Simplify the value of

x

from the given equation, then substitute it into the required expression.

Explanation:

Given:

2x=\sqrt{5}+\frac{1}{\sqrt{5}}

.

Combine the terms:

2x=\frac{5+1}{\sqrt{5}}=\frac{6}{\sqrt{5}}

.

So,

x=\frac{3}{\sqrt{5}}

.

Now,

x^2=\frac{9}{5}

.

Thus,

x^2-1=\frac{9}{5}-1=\frac{4}{5}

.

So,

\sqrt{x^2-1}=\frac{2}{\sqrt{5}}

.

Substitute in

\frac{\sqrt{x^2-1}}{x-\sqrt{x^2-1}}

.

=\frac{\frac{2}{\sqrt{5}}}{\frac{3}{\sqrt{5}}-\frac{2}{\sqrt{5}}}

.

=\frac{\frac{2}{\sqrt{5}}}{\frac{1}{\sqrt{5}}}=2

.

Answer:

2

, so option A is correct.

© examsnet.com

Go to Question:

Prev Question

Next Question