Question

If a =7-4√3, find √a + 1/√a. Answer is 4

Answer 1

Answer:

4

Step-by-step explanation:

Find √a:

a = 7 - 4√3

a = (4 + 3)  - (2 x 2)√3

a = 4 + 3  - 2(2√3)

a = (2)²+ (√3)² - 2(2√3)

a = (2 - √3)²

√a = 2 - √3

Find 1/√a:

1/√a = 1/(2 - √3)

1/√a = 1/(2 - √3) x (2 + √3)/(2 + √3)

1/√a = (2 + √3)/(4 - 3)

1/√a = (2 + √3)

Find √a + 1/√a:

√a + 1/√a = (2 - √3) + (2 + √3)

√a + 1/√a = 2 - √3 + 2 + √3

√a + 1/√a = 4

Answer: 4

Answer 2

Answer :

The required answer is 4.

Step-by-step explanation :

At first, find √a :

a = 7 - 4 √ 3

⇒ a = 4 + 3 - 4 √ 3

⇒ a = (2)² + (√3)² - 2 × 2 × √3

⇒ a = ( 2 + √3 )²

⇒ √a = √(2 + √3)²

⇒ √a = 2 + √3

Now, find 1 / √a :

√a = 2 + √3

⇒ 1 / √a = 1 / 2 + √3

⇒ 1 / √a = 1 / 2 + √3 × 2 - √3 / 2 - √3

⇒ 1 / √a = 2 - √3 / 2² - √3²

⇒ 1 / √a = 2 - √3 / 4 - 3

⇒ 1 / √a = 2 - √3

Finally, add √a + 1 / √a :

√a + 1 / √a = 2 + √3 + 2 - √3

√a + 1 / √a = 2 + 2

√a + 1 / √a = 4

Hence, the required answer is 4.