$\text{Given that,}\\\\x^2 + \dfrac1{x^2} = 38\\\\\\(i)\\\\\left(x-\dfrac 1x \right)^2 = x^2 + \dfrac 1{x^2} - 2 \cdot x \cdot \dfrac 1x\\\\\\\implies \left(x-\dfrac 1x \right)^2 = 38 -2 = 36\\\\\implies x - \dfrac 1x = \pm\sqrt{36} = \pm 6 \\\\\\(ii)\\\\x^2 + \dfrac 1{x^2} = 38\\\\\\\implies \left(x^2 + \dfrac 1{x^2} \right)^2 = 38^2\\\\\\\implies x^4 + \dfrac 1{x^4} + 2\cdot x^2 \cdot \dfrac 1{x^2} = 1444\\\\\\\implies x^4 + \dfrac 1{x^4} + 2 = 1444\\\\\\$

$\implies x^4 +\dfrac 1{x^4} = 1444-2 = 1442$

7 0

2 years ago

Which of the following is an irrational number?

I am Lyosha [343]

Hi!

<h3>An irrational number is a number that cannot be written as a ratio or a fraction. </h3><h3>Let's go through each answer. </h3>

A. √0.036

= 0.18973666...

<u>This is irrational, because it repeats forever.</u>

B. 7.2525

<u>This is rational, because 2525 repeats in a pattern.</u>

C. √1

= 1

<u>This is rational. (1/1)</u>

D. 10

<u>This is rational (10/1)</u>

<h2>The answer is A. √0.036.</h2>

Hope this helps! :)

-Peredhel

7 0

3 years ago