if a=7-4√3 find the value of √a+1\√a
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Answered by
1
- a=7-2root 12
- root a=2-root 3
- 1/root a=2+root3
- by this root a+1/root a =
- 2+root3 +2-root3
- 4 is the answer
Answered by
6
Solution :-
Finding the value of √a
a = 7 - 4√3
⇒ a = 7 - 2(2)(√3)
⇒ a = 4 + 3 - 2(2)(√3)
⇒ a = 2² + (√3)² - 2(2)(√3)
⇒ a = (2 - √3)²
Since a² + b² - 2ab = (a - b)²
Taking square root on both sides
⇒ √a = √(2 - √3)²
⇒ √a = 2 - √3
Finding 1/√a
1/√a = 1/(2 - √3)
Rationalise the denominator
= 1/(2 - √3) * (2 + √3)/(2 + √3)
= {2 + √3}/{2² - (√3)²}
= (2 + √3)/(4 - 3)
= (2 + √3)/1
1/√a = 2 + √3
Findind √a + 1/√a
√a + 1/√a
= 2 - √3 + (2 + √3)
= 2 - √3 + 2 + √3
= 4
Therefore the value of √a + 1/√a is 4
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