Question

1.scrie ca patratul unui binom expresia 3+2√2
2.o banca acorda 4% dobanda lunar.aflati ce suma initiala a depus Alexandra,daca dupa doua luni avea in cont 21632 lei

Answer 1

    
$1) \\ 3+2 \sqrt{2} = \\ =1 + 2+2 \sqrt{2} = \\ = 1 + 2 \sqrt{2} +2= \\ =1^2 + 2\times1\times \sqrt{2} + (\sqrt{2})^2= \\ =\boxed{ (1+\sqrt{2})^2}$


$2) \\ Notatie: \\ x=suma~initiala. \\ Vom~folosi ~formula: ~~~x+4\% \times x = x \times 1,04 \\ \\ Dupa ~doua~luni~avea~in cont: (x \times 1,04) \times 1,04 \\ \\ (x \times 1,04) \times 1,04=21632 \\ \\ \displaystyle (x \times 1,04) = \frac{21632}{1,04} \\ \\ x \times 1,04 = 20800 \\ \\ x=\frac{20800}{1,04} = \boxed{20000 ~Lei~a ~depus~Alexandra~in~cont}$