Question

what is the erithmetic mean √3-√2 and its reciprocal​

Answer 1

Answer:

arithmetic mean of √3-√2 = (√3-√2 )/2 = (1.73 - 1.41)/2=0.32/2 =0.16

arithmetic mean of 1 /√3 -  1/√2 = (1 /√3 -  1/√2)/2

=√2-√3/√2×√3 /2

= (1.73 - 1.41)/(1.73 × 1.41)/2

=0.32/2.4393×2

=0.16/2.4393

Answer 2

SOLUTION

TO DETERMINE

The Arithmetic mean of √3 - √2 and it's reciprocal

EVALUATION

Here the given number is √3 - √2

Now reciprocal of √3 - √2

$\sf \: = \dfrac{1}{ \sqrt{3} - \sqrt{2} }$

$\sf \: = \dfrac{( \sqrt{3} + \sqrt{2} )}{ (\sqrt{3} + \sqrt{2})( \sqrt{3} - \sqrt{2} ) }$

$\sf \: = \dfrac{( \sqrt{3} + \sqrt{2} )}{ {( \sqrt{3} )}^{2} - {( \sqrt{2} )}^{2} }$

$\sf \: = \dfrac{( \sqrt{3} + \sqrt{2} )}{ 3 - 2 }$

$\sf \: = \dfrac{( \sqrt{3} + \sqrt{2} )}{ 1}$

$\sf \: = \sqrt{3} + \sqrt{2}$

Hence the required arithmetic mean

$\sf \: = \dfrac{( \sqrt{3} - \sqrt{2} ) + ( \sqrt{3} + \sqrt{2} )}{ 2}$

$\sf \: = \dfrac{2\sqrt{3} }{ 2}$

$\sf \: = \sqrt{3}$

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