Question

Determine a and b if
Root 7+root5/root 7 -root 5 - root 7 -root 5 /Root 7+root5 = a+root 35 b

Answer 1

Answer:

a=0 and b=\frac{7}{11}

Step-by-step explanation:

The given equation  is :

\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=a+b\sqrt{5}

Solving the LHS of the above equation, we get

\frac{(7+\sqrt{5}(7+\sqrt{5})-(7-\sqrt{5})(7-\sqrt{5})}{49-5}

=\frac{7+5+14\sqrt{5}-7-5+14\sqrt{5}}{44}

=\frac{7}{11}\sqrt{5}

=0+\frac{7}{11}\sqrt{5}

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

a=0 and b=\frac{7}{11}