Question

Simplify (4+√5/4-√5)+(4-√5/4+√5) ?​

Answer 1

Answer:

(4+root 5)^2+(4-root5)

________________________

(4)^2-(root5)^2

(4)^2+root5^2+2×4×root5+(4)^2+root5^2-2×4×root5

____________________________________ 16-5

16+5+8root5+16+5-8root5

__________________________

11

=32+10/11

=42/11Ans

Answer 2

Answer

(4+√5/4-√5)+(4-√5/4+√5)

=>  $4+\sqrt{5}  / 4-\sqrt{5}  * 4+\sqrt{5}  /4+\sqrt{5}$

=> $(4)^2 +(\sqrt{5} )^2 +2(4) (\sqrt{5} ) / (4)^2 +(\sqrt{5} ) ^2 -  2(4) (\sqrt{5}  ) ^2/ (4)^2 +(\sqrt{5} )^2$

=> $16+5+8\sqrt{5} /16-5 +  16+5-8\sqrt{5} /16-5$

=> $21+8\sqrt{5} / 11 + 21-8\sqrt{5} / 11$

=>  $21+8\sqrt{5} + 21-8\sqrt{5}  /11$

=> $21+21/11$

=> $42/11$