Math, asked by BEATSGAMERYT, 2 months ago

(2-√5/2+√5)^2 - (2+√5/2-√5)^2​

Answers

Answered by MrImpeccable
19

ANSWER:

To Solve:

  • (2-√5/2+√5)^2 - (2+√5/2-√5)^2

Solution:

We are given that,

\implies \left(\dfrac{2-\sqrt5}{2+\sqrt5}\right)^2-\left(\dfrac{2+\sqrt5}{2-\sqrt5}\right)^2

Using,

\implies a^2-b^2=(a+b)(a-b)

So,

\implies \left(\dfrac{2-\sqrt5}{2+\sqrt5}\right)^2-\left(\dfrac{2+\sqrt5}{2-\sqrt5}\right)^2

\implies \left(\dfrac{2-\sqrt5}{2+\sqrt5}-\dfrac{2+\sqrt5}{2-\sqrt5}\right)\left(\dfrac{2-\sqrt5}{2+\sqrt5}+\dfrac{2+\sqrt5}{2-\sqrt5}\right)

Taking LCM,

\implies \left(\dfrac{(2-\sqrt5)^2-(2+\sqrt5)^2}{(2+\sqrt5)(2-\sqrt5)}\right)\left(\dfrac{(2-\sqrt5)^2+(2+\sqrt5)^2}{(2+\sqrt5)(2-\sqrt5)}\right)

\implies \left(\dfrac{(4+5-4\sqrt5)-(4+5+4\sqrt5)}{(2)^2-(\sqrt5)^2}\right)\left(\dfrac{(4+5-4\sqrt5)+(4+5+4\sqrt5)}{(2)^2-(\sqrt5)^2}\right)

\implies\left(\dfrac{9-4\sqrt5-9-4\sqrt5}{4-5}\right)\left(\dfrac{9-4\sqrt5+9+4\sqrt5}{4-5}\right)

\implies\left(\dfrac{-8\sqrt5}{-1}\right)\left(\dfrac{18}{-1}\right)

So,

\implies\left(8\sqrt5\right)\left(-18\right)

Hence,

\implies -144\sqrt5

Therefore,

\implies\bf \left(\dfrac{2-\sqrt5}{2+\sqrt5}\right)^2-\left(\dfrac{2+\sqrt5}{2-\sqrt5}\right)^2=-144\sqrt5

Answered by JaideepHarsha
1

Answer:

-144root5

Step-by-step explanation:

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