Question

plzzz solve : (7+root 5)/(7 - root 5 ) - (7 - root 5) / (7 + root 5 ) = a + 7 / 11 × root 5 × b : find a and b.

Answer 1

This is the right answer please mark the brilliant

Step-by-step explanation:

Answer 2

Answer:

The value of a and b are 0 and 2/11 respectively.

Step-by-step explanation:

For first case we use  

Now to rationalize the above value we multiply both the numerator and denominator by $\bold{7+\sqrt{5}}$

$\begin{array}{l}{\left[\frac{7+\sqrt{5}}{7-\sqrt{5}}\right]\left[\frac{7+\sqrt{5}}{7+\sqrt{5}}\right]} \\ {=\frac{7^{2}+\sqrt{5}^{2}+2 \sqrt{5} .7}{49-5}} \\ {=\frac{49+5+14 \sqrt{5}}{44}} \\ {=\frac{54+14 \sqrt{5}}{44}}\end{array}$

For second case we can use

Now to rationalize the above value we multiply $\bold{7-\sqrt{5}}$in numerator and denominator.

$\begin{array}{l}{\left[\frac{7-\sqrt{5}}{7+\sqrt{5}}\right]\left[\frac{7-\sqrt{5}}{7-\sqrt{5}}\right]} \\ {=\frac{7^{2}+\sqrt{5}^{2}-2 \sqrt{5} .7}{49-5}} \\ {=\frac{49+5-14 \sqrt{5}}{44}} \\ {=\frac{54-14 \sqrt{5}}{44}}\end{array}$

Adding both the cases we get  $\frac{54+14 \sqrt{5}}{44}+\frac{54-14 \sqrt{5}}{44}=\frac{14 \sqrt{5}}{11}$

Therefore equating $\frac{14 \sqrt{5}}{11}=a+7 \sqrt{5 b}0+\frac{14 \sqrt{5}}{11}=a+7 \sqrt{5 b}$

We get a = 0 and b =  2/11