Question

If x 2
+ x 2
1
​ =27, find the value of x+1/x

Answer 1

Answer:

Hence, the value of x + 1/x = +29 or' -29.

Step-by-step explanation:

Given:-

x^2 + 1/x^2 = 27

To find out:-

Value of x + 1/x

Solution:-

We have,

x^2 + 1/x^2 = 27

Now, this expression in in the form of;

a^2 + b^2 = (a+b)^2 - 2ab

Where we have to put in our expression a = x and b = 1/x , we get

→ (x + 1/x)^2 - 2(x)(1/x) = 27

→ (x + 1/x)^2 - 2 = 27

→ (x + 1/x)^2 = 27 + 2

→ (x + 1/x)^2 = 29

→ x + 1/x = √29

→ x + 1/x = ±29

Answer:-

Hence, the value of x + 1/x = +29 or' -29.

Used formulae:-

a^2 + b^2 = (a+b)^2 - 2ab

• I hope it's help you!

Answer 2

$\huge\mathcal{\fcolorbox{cyan}{black}{\pink{ANSWER}}}$

Given,

${x}^{2} + \frac{1}{{x}^{2} } = 27$

$x + \frac{1}{x} = \: to \: find$

Now,

$we \: know \: that \\ {x}^{2} + \frac{1}{ {x}^{2} } = {(x + \frac{1}{x} )}^{2} - 2 \times x \times \frac{1}{x} \\ \implies \: 27 = {(x + \frac{1}{x} )}^{2} - 2 \\ \implies \: {(x + \frac{1}{x} )}^{2} = 27 + 2 = 29 \\ \implies \: x + \frac{1}{x} = \pm \: \sqrt{29}$