Question

If a=2+√3, find the value of a-1/a​

Answer 1

Answer:

$\Huge\underline\mathtt{Given\: that :-}$

a = 2+√3

$\mathtt{\huge{\underline{\underline{\red{To\:find\::-}}}}}$

the value of a - 1/a

$\huge\bf\underline\purple{SoLuTiOn:-}$

if a = 2+√3

then $\huge\mathtt\blue{\frac{1}{2}=\frac{1}{2+√3}}$

$\large\mathtt{therefore}$

$\large\mathtt{2+√3-\frac{1}{2+√3}}$

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

$\large\mathtt{\mapsto\frac{6+4\sqrt{3}}{2+\sqrt{3}}}$

$\rm\underline\green{rationalize\: the\: denominator:-}$

$\large\mathtt{\mapsto\frac{6+\sqrt{3}(2-\sqrt{3})}{(2+\sqrt{3})×(2-\sqrt{3})}}$

$\huge\mathtt{\mapsto\frac{12-6\sqrt{3}+8\sqrt{3}-12}{4-3}}$

$\large\mathtt{\mapsto12-6\sqrt{3}+8\sqrt{3}-12}$

$\huge{\boxed{\mathfrak\red{\fcolorbox{magenta}{aqua}{2√3}}}}$

$\Huge\mathfrak\pink{hope\:it\:helps}$

Answer 2

Answer:

the answer is (2√3)

step by step explanation:

a-1/a = (a²-q)/a

putting a= 2+√3

(a²-1)/a = [ (2+√3)²-1]/(2+√3)

= (7+4√3-1)/(2+√3)

= (6+4√3)(2-√3)/ 2²-(√3)²

= (12+8√3-12-6√3) /(4-3)

= (2√3)/(4-3)

= 2√3