Question

Please answer the following attachment. i really need this answer. The Best explanation will be marked brainliest!

2f5d8e91a5179cc4447b2bf08ecfeb53.docx

Answer 1

Step-by-step explanation:

Question:

If $\bold{\dfrac{\sqrt{11}-\sqrt{7} }{\sqrt{11}+\sqrt{7} }=x-y\sqrt{77} ,find\;the\;values\;of\;x\;and\;y. }$

Solution:

• Rationalizing the denominator.

$\mapsto \bold{\dfrac{\sqrt{11}-\sqrt{7} }{\sqrt{11}+\sqrt{7} }\times\dfrac{\sqrt{11}-\sqrt{7}}{\sqrt{11}-\sqrt{7}} }$

$\mapsto \bold{\dfrac{(\sqrt{11}-\sqrt{7})^{2}}{(\sqrt{11^{2})}-(\sqrt{7^{2})}} }$

• (a - b)² = a² + b² - 2ab
• (a + b)(a - b) = a² - b²

$\mapsto \bold{\dfrac{(\sqrt{11})^{2}+(\sqrt{7})^{2}-2(\sqrt{11})(\sqrt{7})}{11-7} }$

$\mapsto \bold{\dfrac{18-2\sqrt{77} }{4} }$

$\mapsto \bold{\dfrac{2(9-\sqrt{77})}{4} }$

$\mapsto \bold{\dfrac{9-\sqrt{77} }{2} }$

• This can be written as.

$\mapsto \bold{\dfrac{9}{2}-\dfrac{\sqrt{77} }{2} =a-b\sqrt{77} }$

• On comparing L.H.S to R.H.S, we get.

$\Rrightarrow \bold{a=\dfrac{9}{2}\;and\;b=\dfrac{1}{2} }$