Question

find the value of a and b if underroot 7-1/underroot 7+1=a+b underroot 7​

Answer 1

Answer:

a=0 and b=\frac{-2}{3}

Step-by-step explanation:

The given equation is:

\frac{\sqrt{7}-1}{\sqrt{7}+1}-\frac{\sqrt{7}+1}{\sqrt{7}-1}=a+b\sqrt{7}

Solving the LHS of the above equation, we get

\frac{(\sqrt{7}-1)^{2}-(\sqrt{7}+1)^{2}}{7-1}

=\frac{7+1-2\sqrt{7}-7-1-2\sqrt{7}}{6}

=\frac{-4}{6}\sqrt{7}

=\frac{-2}{3} \sqrt{7}

Now, comparing with the RHS of the given equation, we get

a=0 and b=\frac{-2}{3}