Question

find the rational number a and b such that:

√11 -√17/√11+√7 = a-b√√77

Answer 1

Answer:

√11-√7÷ √11+√7 =

√11-√7÷√11+√7× √11-√7÷√11-√7

=( √11-√7 )°2 ÷√11°2 -√7°2

=√11°2 +√7°2 -2×√11×√7÷ 11-7

= 11+7-2√77÷ 4 = 18 -2√77÷4

= 9-√77÷ 2 = a-b√77

= a= 9/2 And b = 1/2

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

$\tt{\rightarrow\dfrac{\sqrt{11}-\sqrt{7}}{\sqrt{11}+\sqrt{7}}}$

$\tt{\rightarrow\dfrac{(\sqrt{11}-\sqrt{7})}{(\sqrt{11}+\sqrt{7}})\times\dfrac{(\sqrt{11}-\sqrt{7})}{(\sqrt{11}-\sqrt{7})}}$

$\tt{\rightarrow\dfrac{(\sqrt{11}-\sqrt{7})^{2}}{(\sqrt{11})^{2}-(\sqrt{7})^{2}}}$

$\tt{\rightarrow\dfrac{11+7-2\times\sqrt{11}\times\sqrt{7}}{11-7}}$

$\tt{\rightarrow\dfrac{(18-2\sqrt{11})}{4}$

$\tt{\rightarrow\dfrac{18}{4}-\dfrac{2}{4}\times\sqrt{77}}$

$\tt{\rightarrow\dfrac{9}{2}-\dfrac{1}{2}\times\sqrt{77}}$

$\tt{\rightarrow\dfrac{\sqrt{11}-\sqrt{7}}{\sqrt{11}+\sqrt{7}}=a+b\sqrt{77}}$

$\tt{\rightarrow\dfrac{9}{2}-\dfrac{1}{2}\times\sqrt{77}=a-b\sqrt{77}}$

$\tt{\rightarrow a=\dfrac{9}{2}}$

$\tt{\rightarrow b=\dfrac{1}{2}}$

$\Large{\fbox{Therefore}}$

$\tt{\rightarrow a=\dfrac{9}{2}}$

$\tt{\rightarrow b=\dfrac{1}{2}}$