Question

2a +1 + 12a-1
Y2a +1
prove that - 4ar
If x

Answer 1

Given that,
x=[√(2a+1)+√(2a-1)]/[√(2a+1)-√(2a-1)]

x=[√(2a+1)+√(2a-1)]/[√(2a+1)-√(2a-1)]×{[√(2a+1)+√(2a-1)]/[√(2a+1)+√(2a-1)]}

x=[√(2a+1)+√(2a-1)]²/[{√(2a+1)}²-{√(2a-1)}²]

x=[2a+1+2a-1+2{√(2a+1)(2a-1)}]/[2a+1-2a+1]

x=[4a+2√(4a²-1)]/2

x=2a+√(4a²-1)
Now by putting above value in given equation we have,
=x²-4ax+1

=[2a+√(4a²-1)]²-4a[2a+√(4a²-1)]+1

=4a²+4a²-1+4a√(4a²-1)-8a²-4a√(4a²-1)+1

=8a²-8a²

=0



Hence x²-4ax+1=0 , for given value of x.