Math, asked by 09755, 6 months ago

if p= 2+√3, then find the value of p-1/p

Answers

Answered by Anonymous

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2+√2-1/2+√3

4+3+4√3-1/2+√3

6+4√3/2+√3

Answered by Swarup1998

Given, $p=2+\sqrt{3}$

Now, $\dfrac{1}{2+\sqrt{3}}$

We multiply both the numerator and the denominator by the conjugate irrational number of $(2+\sqrt{3})$ , that is, by $(2-\sqrt{3})$ to rationalize the denominator.

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

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

$=\dfrac{2-\sqrt{3}}{4-3}$

$=2-\sqrt{3}$

Then, $p-\dfrac{1}{p}$

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

$=2+\sqrt{3}-2+\sqrt{3}$

$=2\sqrt{3}$

#SPJ3

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