Question

сравните числа a и b, если a= __1__ _ __1__ , b= 5.5 3-2√2 3+2√2

Answer 1

 

$a = \frac{1}{3 - 2\sqrt[]{2}} - \frac{1}{3 + 2\sqrt[]{2}}$

 

 

 

$a = \frac{3+2\sqrt[]{2}}{9-8} - \frac{3-2\sqrt[]{2}}{9-8}$

 

 

 

$a = 3+2\sqrt{2} - (3-2\sqrt{2}) = 3+2\sqrt{2} - 3+ 2\sqrt{2}$ = $4\sqrt{2}$ = $\sqrt{32}$

 

 

b = 5,5 = $\sqrt{30,25}$    

 

$\sqrt{30,25} < \sqrt{32}$

 

$b<a$