Question

please sen the answer quickly ​

Answer 1

ɢɪᴠᴇɴ:

• a = 7-4√3 .

ᴛᴏ ғɪɴᴅ:

• The value of √a + 1/√a.

ᴀɴsᴡᴇʀ:

Firstly it's given that a = 7-4√3

So, 1/a = 1/7-4√3

Let's rationalise the denominator,

=> 1/a = 1 / 7-4√3.

=> 1/a = 1 ( 7+4√3)/(7-4√3)(7+4√3).

=> 1/a = 7+4√3 / 7² - (4√3)².

=> 1/a = 7+4√3 / 49-48.

=> 1/a = 7+4√3 .

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Let , 1/√a + √a = x .

=> 1/√a + √a = x .

=> ( 1/√a + √a ) ² = x².

=> (1/√a)² + (√a)² + 2 × 1/√a × √a = x².

=> 1/a + a +2 = x².

=> (7-4√3)+(7+4√3) = x²

=> 7 + 7 + 2 = x².

=> x² = 16.

=> x = √16.

=> x = ± 4.

Hence the required answer is ±4.