Question

solve as soon as possible​

Answer 1

I think it's answer is 0

Answer 2

GIVEN:-

• $\rm{\dfrac{7 + \sqrt{5}}{7-\sqrt{5}} - \dfrac{7 - \sqrt{5}}{7 + \sqrt{5}}}$.

TO FIND:-

• The Value of given Problem.

HOW TO SOLVE:-

• Firstly, we will solve the problem by solving them separately by Rationalisation method.

• After find the value seperately we will subtract them.

Now,

$\rm{\dfrac{7 + \sqrt{5}}{7-\sqrt{5}}\times{\dfrac{7+\sqrt{5}}{{7+\sqrt{5}}}}}$

$\rm{\dfrac{(7 + \sqrt{5})^2}{49-5}}$

$\rm{\dfrac{49 + 14\sqrt{5} + 5}{44}}$

$\rm{ {\dfrac{54+ 14\sqrt{5}}{44}}}$.

Again

$\rm{\dfrac{7 - \sqrt{5}}{7+\sqrt{5}}\times{\dfrac{7-\sqrt{5}}{{7-\sqrt{5}}}}}$

$\rm{\dfrac{(7 - \sqrt{5})^2}{49-5}}$

$\rm{\dfrac{49 - 14\sqrt{5} + 5}{44}}$

$\rm{ \dfrac{54- 14\sqrt{5}}{44}}$.

Now,

$\rm{ \dfrac{54+ 14\sqrt{5}}{44} - \dfrac{(54- 14\sqrt{5})}{44}}$

$\rm{ \dfrac{54 + 14\sqrt{5} - 54+14\sqrt{5}}{44}}$

$\rm{ \dfrac{ 28\sqrt{5}}{44}}$.

Hence, The value is 28√5/44.