1 Answer

Wu Zhou · Answer 1 · 2022-03-11T15:54:51+0000

Question:-

If a = 6 -
√(35) , find the value of a² +
(1)/(a²)

a = 6 -
√(35) (Given)

Now, first of all we have to find the value of
(1)/(a) .

So,
(1)/(a) =
$(1)/(6 \: - \: √(35))$

(1)/(a) =
$(6 \: + √(35))/((6 \: - \: √(35))(6 \: + \: √(35)))$

(1)/(a) =
$(6 \: + √(35))/((6)² \: - \: (√(35))²)$

(1)/(a) =
$(6 \: + √(35))/(36 \: - \: 35)$
$(\because √(35) \: × \: √(35) \: = \: 35)$

(1)/(a) =
$(6 \: + \: √(35))/(1)$

(1)/(a) = 6 +
√(35)

Now, we have to find the value of a² +
(1)/(a²)

So, a² +
(1)/(a²) =
$(a \: + (1)/(a))²$ - 2.a.
(1)/(a)

a² +
(1)/(a²) =
$(6 \: - √(35) \: + \: 6 \: + √(35))²$ - 2

a² +
(1)/(a²) = (12)² - 2

a² +
(1)/(a²) = 144 - 2

a² +
(1)/(a²) = 142

The value of a² +
(1)/(a²) is 142. [Answer]