Question

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

Answer 1

Answer:

x + 1/x = 5 1/5 = 26/5

26 = 25+1 = 5²+1

x+1/x = (x²+1)/x = (5²+1)/5

So x = 5

Answer 2

Step-by-step explanation:

Given:

$x + \frac{1}{x} = 5 \frac{1}{5}$

To find: Value of x.

Solution:

Tip: Convert mixed fraction into improper fraction.

*Improper fraction is in p/q form, where p>q, during conversion multiplying the denominator with the whole number and add the numerator.

Step 1: Take LCM into LHS and convert mixed fraction into improper in RHS

$\frac{ {x}^{2} + 1}{x} = \frac{26}{5}$

Step 2: Cross multiply

$5( {x}^{2} + 1) = 26x$

or

$5 {x}^{2} - 26x + 5 = 0$

Step 3: Factorise by splitting middle term

$5 {x}^{2} - 25x - x + 5 = 0$

or

$5x(x - 5) - 1(x - 5) = 0$

or

$(5x - 1)(x - 5) = 0$

or

$5x - 1 = 0$

Thus,

$x = \frac{1}{5}$

or

$(x - 5) = 0$

Thus,

$x = 5$

Final answer:

$\bf x = \frac{1}{5}$

$\bf x = 5$

Hope it helps you.

To learn more:

1) Solve the given quadratic equation:

3x² - 7x + 5 = 0

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2) The product of two consecutive positive integers is 42 what are the integers

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