Question

plz answer this question​

Answer 1

$\Large{\underline{\underline{\red{\tt{\purple{\leadsto } GiveN:-}}}}}$

• $\sf a = \dfrac{ 2-\sqrt3}{2+\sqrt3}$
• $\sf b = \dfrac{2+\sqrt3}{2-\sqrt3}$

$\Large{\underline{\underline{\red{\tt{\purple{\leadsto } To\:FinD:-}}}}}$

• $\sf The\:value\:of\:a^2-b^2$

$\Large{\underline{\underline{\red{\tt{\purple{\leadsto } AnsweR:-}}}}}$

Let's firsrt simplify a & b for easy calculation .

$\underline{\green{\orange{\mapsto} \sf Simplifying\:a :-}}$

$\tt :\implies a = \dfrac{ 2-\sqrt3}{2+\sqrt3}$

$\tt :\implies a=\bigg\lgroup \dfrac{ (2-\sqrt3)(2-\sqrt3)}{(2+\sqrt3)(2-\sqrt3)} \bigg\rgroup$

$\tt :\implies a= \bigg\lgroup \dfrac{ (2-\sqrt3)^2}{(2)^2-(\sqrt3)^2} \bigg\rgroup$

$\tt :\implies a= \bigg\lgroup \dfrac{ (2-\sqrt3)^2}{4-3}\bigg\rgroup$

$\tt :\implies a= \bigg\lgroup \dfrac{ (2-\sqrt3)^2}{1}\bigg\rgroup$

$\boxed{\bf\red{\hookrightarrow}\:a=(2-\sqrt3)^2}$

___________________________________

$\underline{\green{\orange{\mapsto} \sf Simplifying\:b :-}}$

$\tt :\implies b = \dfrac{ 2+\sqrt3}{2-\sqrt3}$

$\tt :\implies b=\bigg\lgroup \dfrac{ (2+\sqrt3)(2+\sqrt3)}{(2-\sqrt3)(2-\sqrt3)} \bigg\rgroup$

$\tt :\implies b= \bigg\lgroup \dfrac{ (2+\sqrt3)^2}{(2)^2-(\sqrt3)^2} \bigg\rgroup$

$\tt :\implies b= \bigg\lgroup \dfrac{ (2+\sqrt3)^2}{4-3}\bigg\rgroup$

$\tt :\implies b= \bigg\lgroup \dfrac{ (2+\sqrt3)^2}{1}\bigg\rgroup$

$\boxed{\bf\red{\hookrightarrow}\:b=(2+\sqrt3)^2}$

___________________________________

$\underline{\green{\orange{\mapsto} \sf Now\: let's\:simplify\:a^2-b^2:-}}$

$\tt:\implies a^2-b^2=(a+b)(a-b)$

$\tt:\implies a^2-b^{2}=[(2-\sqrt3)^2+(2+\sqrt3)^2][(2-\sqrt3)^2-(2+\sqrt3)^2]$

$\tt:\implies a^2-b^2=(4+3-4\sqrt3+4+3+4\sqrt3)[4+3-4\sqrt3-(4+3+4\sqrt3)]$

$\tt:\implies a^2-b^2=(7+7)(7-4\sqrt3-7-4\sqrt3)$

$\tt:\implies a^2-b^2=14\times (-8\sqrt3)$

$\underline{\boxed{\red{\tt\longmapsto a^2-b^2=(-112\sqrt3)}}}$

$\boxed{\purple{\bf\pink{\dag}\:Hence\:the\: required\:answer\:is\:(-112\sqrt3).}}$

Answer 2

Step-by-step explanation:

a2-b2

hope you understand