Question

find the value of a and b if 3+√7/3-√7=a+b√7​

Answer 1

Step-by-step explanation:

$\frac{3+\sqrt{7} }{3-\sqrt{7} } *\frac{3+\sqrt{7} }{3+\sqrt{7} } =\frac{(3+\sqrt{7})(3+\sqrt{7} ) }{(3)^{2}-(\sqrt{7} ) ^{2} }$

$\frac{9+3\sqrt{7}+3\sqrt{7} +7 }{9-7}$

$\frac{9+7+3\sqrt{7}+3\sqrt{7} }{2}$

$\frac{16+6\sqrt{7} }{2}$

$\frac{2(8+3\sqrt{7}) }{2}$

2 from both numerator and denominator will be cancelled.

∴$8+3\sqrt{7} =a+b\sqrt{7}$

∴a=8 and b=3

Hope this helps you