Question

can sm1 solve this??

Answer 1

Answer:

9

Step-by-step explanation:

First, we need to rationalize the denominators of the given values of a and b.

⇒ $a = \frac{\sqrt{11} - \sqrt{7}}{\sqrt{11} + \sqrt{7}} * \frac{\sqrt{11} - \sqrt{7}}{\sqrt{11} - \sqrt{7}}$       and        $b = \frac{\sqrt{11} + \sqrt{7}}{\sqrt{11} - \sqrt{7}} * \frac{\sqrt{11} + \sqrt{7}}{\sqrt{11} + \sqrt{7}}$

We know that, (a±b)² = a² ± 2ab + b     and     (a+b)(a-b) = a² - b²

⇒ $a = \frac{11 - 2\sqrt{77} + 7}{11 - 7}$              and             $b = \frac{11 + 2\sqrt{77} + 7}{11 - 7}$

⇒ $a = \frac{18 - 2\sqrt{77}}{4}$                 and              $b = \frac{18 + 2\sqrt{77}}{4}$

⇒ $a = \frac{2[9 - \sqrt{77}]}{2 * 2}$                 and              $b = \frac{2[9 + \sqrt{77}]}{2 * 2}$

⇒ $a = \frac{9 - \sqrt{77}}{2}$                    and              $b = \frac{9 + \sqrt{77}}{2}$

∴ $a + b = \frac{9 - \sqrt{77}}{2} + \frac{9 + \sqrt{77}}{2}$

           ⇒ $\frac{9 - \sqrt{77} + 9 + \sqrt{77}}{2}$

           ⇒ $\frac{18}{2}$

           ⇒ $9$

Hope it helps...

Thanks