Math, asked by Siddhi2158, 3 months ago

If a=2+√3, then value of a+1/a​

Answers

Answered by shashank35132
0

Answer:

4

Step-by-step explanation:

a = 2 + \sqrt{3}

therefore,

a + \frac{1}{a} \\= [2+\sqrt{3} ] +\frac{1}{2+\sqrt{3}} \\= [2+\sqrt{3} ] + \frac{1(2 - \sqrt{3}) }{(2 + \sqrt{3})(2 - \sqrt{3})} \\= [2+\sqrt{3} ] + \frac{2 - \sqrt{3}}{2^{2} - (\sqrt{3})^{2} } \\=  [2+\sqrt{3} ]  + \frac{2 - \sqrt{3}}{4-3} \\= 2 + \sqrt{3} + \frac{2 - \sqrt{3}}{1}\\= 2 + \sqrt{3} + {2 - \sqrt{3}}\\= 4+ 0\\= 4

Answered by tennetiraj86
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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