If a=2+√3, then value of a+1/a
Answers
Answered by
0
Answer:
4
Step-by-step explanation:
therefore,
Answered by
1
Step-by-step explanation:
Given :-
a = 2 + √3
To find :-
Find the value of a + (1/a) ?
Solution:-
Given that :
a = 2 + √3
=> 1/a = 1/(2+√3)
Denominator = 2+√3
We know that
The Rationalising factor of a+√b is a-√b
The Rationalising factor of 2+√3 is 2-√3
On Rationalising the denominator then
=> 1/a = [1/(2+√3)]×[(2-√3)/(2-√3)]
=> 1/a = (2-√3)/(2+√3)(2-√3)
=> 1/a = (2-√3)/(2^2-(√3)^2))
Since (a+b)(a-b)=a^2-b^2
Where a = 2 and b =√3
=> 1/a = (2-√3)/(4-3)
=>1/a = (2-√3)/1
=> 1/a = 2-√3
Now the value of a +(1/a)
=>a+(1/a)
=> (2+√3)+(2-√3)
=> 2+√3+2-√3
=> (2+2)+(√3-√3)
=> 4+0
=> 4
Answer:-
The value of a+(1/a) for the given problem is 4
Used formulae:-
- The Rationalising factor of a+√b is a-√b
- (a+b)(a-b)=a^2-b^2
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