Question

X is equals to 2 minus root 5 upon 2 + root 5 and Y is equals to 2 + root 5 upon 2 minus root 5 find the value of x square minus y square

Answer 1

Answer:

$\frac{11}{4}+2\sqrt{5}$

Step-by-step explanation:

First we need to properly define our Equalities:

$x=2-\frac{\sqrt{5} }{2}+\sqrt{5}\\ y=2+\frac{\sqrt{5} }{2}-\sqrt{5}$

Now, we need to define the problem:

$x^{2} +y^{2}$

To simplify its resolution, we will solve each  square separately:

$x^{2} =(2-\frac{\sqrt{5} }{2}+\sqrt{5})^{2} =(2-\frac{\sqrt{5} }{2}+\sqrt{5})(2-\frac{\sqrt{5} }{2}+\sqrt{5})=\\ 4-2\frac{\sqrt{5} }{2}+2\sqrt{5}-2\frac{\sqrt{5} }{2}+\frac{5}{4}-\frac{5}{2}+2\sqrt{5}-\frac{5}{2}+5=\\ 4+5+\frac{5}{4}-\frac{5}{2} -\frac{5}{2}-2\frac{\sqrt{5} }{2}}-2\frac{\sqrt{5} }{2}+2\sqrt{5}+2\sqrt{5}=\\ \frac{11}{4}+2\sqrt{5}$

Answer 2

Answer:

-144√5

Hey guys!

I hope this answer and procedure helps you.