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Dmitriy789 [7]
2 years ago
11

If x = 5-2√6, find the value of:(i) x + 1/x(ii) x² + 1/x²Please solve ASAP​

Mathematics
1 answer:
Vitek1552 [10]2 years ago
5 0

Answer:

  1. x+(1/x) = 10 and
  2. x²+ (1/x²) = 98

Step-by-step explanation:

Given that :

x = 5-2√6

1/x = 1/(5-2√6)

The denominator = 5-2√6

The Rationalising factor of 5-2√6 = 5+2√6

On Rationalising the denominator then

⇛ 1/x = [1/(5-2√6)]×[(5+2√6)/5+2√6)]

⇛ 1/x = (5+2√6)/[5-2√6)(5+2√6)]

⇛ 1/x = (5+2√6)/[5²-(2√6)²]

Since (a+b)(a-b) = a²-b²

Where ,

  • a = 5 and
  • b = 2√6

⇛1/x = (5+2√6)/(25-24)

⇛ 1/x = (5+2√6)/1

⇛ 1/x = 5+2√6

Now,

x +(1/x)

⇛ 5-2√6+5+2√6

⇛ 5+5

⇛ 10

Therefore, x+(1/x) = <u>10</u><u>.</u>

On squaring both sides then

⇛ [x+(1/x)]² = 10²

⇛ x²+2(x)(1/x)+(1/x)² =100

⇛ x²+2+(1/x)² = 100

⇛ x²+(1/x²) = 100-2

⇛ x²+(1/x²) = 98

Therefore, x²+(1/x²) = <u>98.</u>

<u>Read </u><u>more</u><u>:</u>

Similar questions;

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brainly.com/question/24697983?referrer

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