4+5 +5 x underoot of 9
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Answer:
24
Step-by-step explanation:
Step-by-step explanation:
Given x = 9 + 4√5.
⇒ 4 + 5 + 2 * 2 * √5
⇒ (2)^2 + (√5)^2 + 2 * (2) * (√5)
It is in the form of a^2 + b^2 + 2ab = (a + b)^2.
⇒ (2 + √5)^2.
So, x = (2 + √5)^2.
Then, √x = (2 + √5).
Now,
= > \frac{1}{\sqrt{x}}=>
x
1
= > \frac{1}{(2 + \sqrt{5})} * \frac{(2 - \sqrt{5})}{(2 - \sqrt{5})}=>
(2+
5
)
1
∗
(2−
5
)
(2−
5
)
= > \frac{(2 - \sqrt{5})}{(2)^2 - (\sqrt{5})^2}=>
(2)
2
−(
5
)
2
(2−
5
)
= > \frac{2 - \sqrt{5}}{4 - 5}=>
4−5
2−
5
= > \frac{2 - \sqrt{5}}{-1}=>
−1
2−
5
= > \sqrt{5} - 2=>
5
−2