Question

Determinati a)√2 /1+√2= a+b√2
b)√3/√2+√3=c+d√6

Answer 1

$\frac{ \sqrt{2}}{1+ \sqrt{2} } = \frac{ \sqrt{2}(1- \sqrt{2}) }{(1+ \sqrt{2})(1- \sqrt{2}) }= \frac{ \sqrt{2}-2 }{1-2}=2- \sqrt{2}=a+b \sqrt{2},deci,a=2$
si b=-1.
b) $\frac{ \sqrt{3} }{ \sqrt{2}+ \sqrt{3} }=$,amplificam cu conjugata √3-√2, si obtinem = (√3) (√3-√2)=
3-√6=c+d√6, deci c=3 si d=-1