Question

if a=2+√3, then find the value of a-1\a​

Answer 1

Answer:

2√3

Step-by-step explanation:

a = 2+√3_______(1)

1/a = 1/2+√3

Rationalise it,

1/a = 1/2+√3×2-√3/2-√3

= 2-√3/(2)²-(√3)²

= 2-√3________(2)

so, a+1/a = 2+√3-2+√3=2√3 from (1) and (2) equation

______________________

Hope it's helpful

Answer 2

AnSwEr

√3 - 1

QuEsTiOn :-

if a=2+√3, then find the value of a-1\a.

SoLuTiOn :-

Given

a = 2 + √3

then ,

$\frac{a - 1}{a} \\ \\ putting \: a \: = 2 + \sqrt{3} \\ \\ = \frac{2 + \sqrt{3} - 1 }{2 + \sqrt{3} } \\ \\ = \frac{ 1 + \sqrt{3} }{2 + \sqrt{3} } \\ \\ by \: rationalising \: the \: denominator \: \\ \\ = \frac{(1 + \sqrt{3}) \times (2 - \sqrt{3} )}{(2 + \sqrt{3} ) \times (2 - \sqrt{3} )} \\ \\ = \frac{1(2 - \sqrt{3} ) + \sqrt{3} (2 - \sqrt{3} )}{ {(2)}^{2} - {( \sqrt{3}) }^{2} }$

By using identify=>

(a - b) (a + b) = a² - b²

$= \frac{2 - \sqrt{3} + 2 \sqrt{3} - 3}{4 - 3} \\ \\ = \sqrt{3} - 1$

Therefore,

${\purple{\boxed{\large{\bold{The \: value \: of \: \frac{a - 1}{a \: } = \sqrt{3} - 1 }}}}}$