Question

if a is equal to 2 minus root 5 divided by 2 + root 5 is equal to 2 + root 5 divided by 2 minus root 5 then find the value of a square minus b square

Answer 1

on solving it further
= (-18/1)(8√5/1)
= -144√5

Answer 2

$a^2-b^2=-144 \sqrt{5}$

Step-by-step explanation:

Given data:

$a=\frac{2-\sqrt{5} }{2+\sqrt{5} } , \ \ b=\frac{2+\sqrt{5} }{2-\sqrt{5} }$

To find a² - b²:

$a^2-b^2=\left(\frac{2-\sqrt{5}}{2+\sqrt{5}}\right)^2-\left(\frac{2+\sqrt{5}}{2-\sqrt{5}}\right)^2$

           $=\frac{(2-\sqrt{5} )^2}{(2+\sqrt{5} )^2} -\frac{(2+\sqrt{5} )^2}{(2-\sqrt{5} )^2}$

Using identity: $(a+b)^2=a^2+2ab+b^2$ and $(a-b)^2=a^2-2ab+b^2$

If we expand using the identity, we get

          $=\frac{9-4 \sqrt{5}}{9+4 \sqrt{5}}-\frac{9+4 \sqrt{5}}{9-4 \sqrt{5}}$  

To make the denominator same, multiply and divide by common factor.

         $=\frac{(9-4 \sqrt{5})^{2}}{(9+4 \sqrt{5})(9-4 \sqrt{5})}-\frac{(9+4 \sqrt{5})^{2}}{(9+4 \sqrt{5})(9-4 \sqrt{5})}$      

        $=\frac{-144 \sqrt{5}}{1}$

$a^2-b^2=-144 \sqrt{5}$

To learn more...

1. if a is equal to 2 minus root 5 divided by 2 + root 5 is equal to 2 + root 5 divided by 2 minus root 5 then find the value of a square minus b square

https://brainly.in/question/2575674

2. If 3 divided by 4 square root 5 minus root 3 + 2 / 4 square root 5 + root 3 is equal to a square root 5 + b square root 3 then find the value of a and b

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