Question

a+b✓2=3+2✓2/3-2✓2 find the value of a and b​

Answer 1

Answer:

Hey Mate!!

$a + b\sqrt{2} = \frac{3+2\sqrt{2} }{3-2\sqrt{2} } \\\\\implies a + b\sqrt{2} = \frac{(3+2\sqrt{2})^{2} }{(3-2\sqrt{2} )(3+2\sqrt{2}) }\\\\\implies a + b\sqrt{2} = \frac{3^{2} + 2(3)(2\sqrt{2})+(2\sqrt{2}) ^{2} }{3^{2}-(2\sqrt{2})^{2} } }\\\\\implies a + b\sqrt{2} = \frac{9+12\sqrt{2}+8 }{9 - 8} \\\\\implies a + b\sqrt{2} = \frac{17 + 12\sqrt{2} }{1} \\\\\implies a + b\sqrt{2} = 17 + 12\sqrt{2}\\\\\therefore \boxed{\bold{a = 17,\:b=12}}$