Question

(7+ root 5/ 7 - root 5) -( 7 - root 5/ 7+ root 5)= a+b root 5

Answer 1

$(7+\frac{\sqrt5}7-\sqrt5)-(7-\frac{\sqrt5}7+\sqrt5)=a+b\sqrt5\\7+\frac{\sqrt5}7-\sqrt5-7+\frac{\sqrt5}7-\sqrt5=a+b\sqrt5\\\frac{2\sqrt5}7-2\sqrt5=a+b\sqrt5\\\frac{2\sqrt5-14\sqrt5}7=a+b\sqrt5\\0+\frac{-12\sqrt5}7=a+b\sqrt5\\a=0\\b=\frac{-12}7$