Question

if x is equal to under root 5 minus 2 over under root 5 + 2 and Y is equal to under root 5 + 2 over under root 5 minus 2 show that x square minus y square is equal to minus 144 under root 5 ​

Answer 1

Answer:

prrof...  -144 sqrt 5.

Step-by-step explanation:

Given x = (√5 - 2) /(√5 + 2),        y = (√5 +2 )/ (√5 - 2)

To show that x² - y² = -144 √5.

 

   We can do it in two ways.      One way is by rationalizing x and y, then squaring them, and then finding x² - y².   Second way is by finding x + y and x - y and then multiplying them.

$x + y = \frac{\sqrt5 -2}{\sqrt5 +2} + \frac{\sqrt5 +2}{\sqrt5 -2}\\\\=\frac{(\sqrt5-2)^2+(\sqrt5+2)^2}{(\sqrt5)^2-(2)^2}\\\\=\frac{5+4+5+4}{1}=18\\\\x - y = \frac{\sqrt5 -2}{\sqrt5 +2} - \frac{\sqrt5 +2}{\sqrt5 -2}\\\\=\frac{(\sqrt5-2)^2-(\sqrt5+2)^2}{(\sqrt5)^2-(2)^2}\\\\=\frac{-2*2 \sqrt5 - 2 *2 \sqrt5}{1}=-8 \sqrt5\\\\So \ x^2 -  y^2 = - 8 * 18 * \sqrt5 = -144 \sqrt5$

So answer.

Answer 2

Answer:

it is given dude..........