Question

find the value of a and b if
7+√5 - 7-√5 = a+√5b
7-√5    7+√5

please solve it

Answer 1

$\frac{7+\sqrt5}{7-\sqrt5}-\frac{7-\sqrt5}{7+\sqrt5}=a+\sqrt5\ b\\\\rationalize\ the\ fractions\\\\\frac{7+\sqrt5}{7-\sqrt5}*\frac{7+\sqrt5}{7+\sqrt5}-\frac{7-\sqrt5}{7+\sqrt5}*\frac{7-\sqrt5}{7-\sqrt5}=a+\sqrt5\ b\\\\\frac{(7+\sqrt5)^2}{7^2-(\sqrt5)^2}-\frac{(7-\sqrt5)^2}{7^2-(\sqrt5)^2}=a+\sqrt5\ b\\\\\frac{49+5+14\sqrt5}{49-5}-\frac{49+5-14\sqrt5}{49-5}=a+\sqrt5\ b\\\\\frac{28\sqrt5}{44}=a+\sqrt5\ b\\\\\So\ \ a=0\\\\b=28/44=7/11$