1a)3a√2-2a+5b√2-3b=7√2-5
3a√2+5b√2-2a-3b=7√2-5
√2(3a+5b)-2a-3b=-5
Identificam coeficienti si vom obtine sistemul:
[tex] \left \{ {{3a+5b=7=2} \atop {-2a-3b=-5}} \right. [/tex]⇔[tex] \left \{ {{6a+10b=14} \atop {-6a-9b=-15}} \right. [/tex]
Le adunam si vom obtine:
b=-1
3a+5b=7
3a-5=7
3a=12⇒a=4
b)[tex] \frac{1}{1+ \sqrt{2} }+ \frac{1}{ \sqrt{2} + \sqrt{3} } +...+ \frac{1}{ \sqrt{n} + \sqrt{n+1} }=26 \\
\frac{1}{ \sqrt{2}+1 } + \frac{1}{ \sqrt{3}+ \sqrt{2} }+...+ \frac{1}{
\sqrt{n+1} + \sqrt{n} }=26
[/tex]
Rationalizam si obtinem:
√2-1+√3-√2+....+√n+1-√n=26
Vom avea:-1+√n+1=26
√n+1=27
Ridicam la patrat:n+1=729
n=728
