Question

If a = 2+ √3, find the value of a -1÷a​

Answer 1

Answer:

2√3

Step-by-step explanation:

Given-----> a = 2 + √3

To find ------> ( a - 1 / a )

Solution------> a = 2 + √3

1 / a = 1 / ( 2 + √3 )

Multiplying in numerator and denominator by conjugate of denominator which is ( 2 - √3 ) .

=> 1 / a = ( 2 - √3 ) / ( 2 + √3 ) ( 2 - √3 )

We have an identity ,

a² - b² = ( a + b ) ( a - b ) , applying it in denominator , we get,

= ( 2 - √3 ) / ( 2 )² - ( √3 )²

= ( 2 - √3 ) / ( 4 - 3 )

= ( 2 - √3 ) / 1

=> 1 / a = ( 2 - √3 )

Now,

a - 1 / a = ( 2 + √3 ) - ( 2 - √3 )

= 2 + √3 - 2 + √3

+2 and -2 cancel out each other, and we get,

=> a - 1 / a = 2√3

Answer 2

your question:

If a = 2+ √3, find the value of a -1÷a

answer with step by step explanation:

according to the question a is equal to 2 + root 3

a=2+√3

then,

a -1÷a = (2+√3) - 1 ÷ (2 +√3)

$(2 + \sqrt{3} ) - \frac{1}{(2 + \sqrt{3} )} \\ = \frac{ {(2 + \sqrt{3}) }^{2} - 1}{(2 + \sqrt{3} )} \\ = \frac{ {2}^{2} + { \sqrt{3} }^{2} + 2 \times 2 \times \sqrt{3} - 1}{(2 + \sqrt{3}) } \\ = \frac{4 + 3 + 4 \times \sqrt{3} - 1 }{(2 + \sqrt{3} )} \\ = \frac{7 - 1 + 4 \times \sqrt{3} }{(2 + \sqrt{3} )} \\ = \frac{6 + 4 \times1.7320508076}{(2 + \sqrt{3} )} \\ = \frac{6 +6.9282032304}{(2 + \sqrt{3}) } \\ = \frac{12.9282032304}{(2 + \sqrt{3}) } \\ = 1.8564064606$

hence,the value of a -1÷a = 1.8564064

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