Question

Va rog frumos sa imi rezolvati si mie ex 4 si 5 !

Answer 1

$a=\frac{1}{\sqrt{2}}+\frac{2}{2 \sqrt{2}}+ \frac{3}{3\sqrt{2}}+\frac{4}{4\sqrt{2}}=\frac{1}{\sqrt2}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}=\\ \frac{4}{\sqrt{2}}=\frac{4\sqrt{2}}{2}=2\sqrt{2}\\ \\ b = \frac{\sqrt{13^{2}-5^{2}}}{\sqrt{10^{2}-8^{2}}}=\frac{\sqrt{169-25}}{\sqrt{100-64}}=\frac{\sqrt{144}}{\sqrt{36}}=\frac{12}{6}=2\\ \\ b)\ a^{2}-b^{2}= ? \\ a^{2}-b^{2} = (2\sqrt{2})^{2}-2^{2}=8-4 = 4\\ \\ E(x) =x^{3}+(x+1)^{2}+2(x-3)(x+3)+17 =\\x^{3}+x^{2}+2x+1+2(x^{2} -9)+17=\\x^{3}+x^{2}+2x+1+2x^{2}-18+17= \\ x^{3}+3x^{2}+2x = x(x^{2}+3x+2)=\\ x(x^{2}+2x+x+2=\\x(x+1)(x+2)\\ \\ \\ \\ E(n) = n(n+1)(n+2)\ divizibil \ cu \ 6$
(produsul a oricaror 3 numere nat. consecutive este divizibil cu 6)