Question

Rationalise: i) 5

√7- √5

ii) If a= 7- 4 √3 then find the value of a + 1/a​

Answer 1

ii) 14

Step-by-step explanation:

Given:

a = 7 - 4√3

To find:

$a + \dfrac{1}{a}$

Solution:

$a = 7 - 4 \sqrt{3} \\ \\ \frac{1}{a} = 7 - 4 \sqrt{3} \\ \\ [\text{Rationalizing the denominator}] \\ \\ = \frac{(7 + 4 \sqrt{3} )}{(7 - 4 \sqrt{3})(7 + 4 \sqrt{3})} \\ \\ = \frac{7 + 4 \sqrt{3} }{ {(7)}^{2} - {(4 \sqrt{3}) }^{2}} \\ \\ = \frac{7 + 4 \sqrt{3} }{49 - 16 \times 3} \\ \\ = \frac{7 + 4 \sqrt{3} }{49 - 48} \\ \\ = \frac{7 + 4 \sqrt{3} }{1} \\ \\ = 7 + 4 \sqrt{3}$

Now,

$a + \frac{1}{a} = 7 - 4 \sqrt{3} + 7 + 4 \sqrt{3} \\ \\ = 7 + 7 \\ \\ = 14$

The required answer is 14.

Answer 2

Answer:

(i) 5(root7 + root5) / 24

(ii) 14

Step-by-step explanation:

Please go through the process and answer .

Thank you!