Matematică, întrebare adresată de cvrogdogcvjp, 8 ani în urmă

va roooooog!!!!❤❤❤❤ am nevoie urgent

Anexe:

albatran: si altele mai usoare nu ai primit?

cvrogdogcvjp: ba da, cred

albatran: adica asta, daca nu se uita unul mai istet decat mine sisa ti-o faca, daca nu o faci , si tu esti elev mediu....nu te va sanctiona nimeni daca nu o ai facuta

albatran: si iti face pecelelate, mai usoare,. din care poti si invata

cvrogdogcvjp: :>

cvrogdogcvjp: <3

cvrogdogcvjp: pup

albatran: mci, asemenea..primesc!! dar eu totcred ca cine a copiat problema nu a copiat-o bine..

cvrogdogcvjp: profa a scris problema, ea a trimiso pe gru0

cvrogdogcvjp: grup

Răspunsuri la întrebare

Răspuns de tcostel

$\displaystyle\\a=\sqrt{6-\sqrt{35}}-\sqrt{6+\sqrt{35}}\\\\\text{Aplicam formulele:}\\\\\sqrt{a+\sqrt{b}}=\sqrt{\frac{a+\sqrt{a^2-b}}{2}}+\sqrt{\frac{a-\sqrt{a^2-b}}{2}}\\\\\\\sqrt{a-\sqrt{b}}=\sqrt{\frac{a+\sqrt{a^2-b}}{2}}-\sqrt{\frac{a-\sqrt{a^2-b}}{2}}$

$\displaystyle\\\text{Rezolvare:}\\\sqrt{6-\sqrt{35}}=\sqrt{\frac{6+\sqrt{6^2-35}}{2}}-\sqrt{\frac{6-\sqrt{6^2-35}}{2}}=\\=\sqrt{\frac{6+\sqrt{36-35}}{2}}-\sqrt{\frac{6-\sqrt{36-35}}{2}}=\\=\sqrt{\frac{6+1}{2}}-\sqrt{\frac{6-1}{2}}=\boxed{\sqrt{\frac{7}{2}}-\sqrt{\frac{5}{2}}}\\\\\text{Prin analogie rezulta:}\\\sqrt{6+\sqrt{35}}=\boxed{\sqrt{\frac{7}{2}}+\sqrt{\frac{5}{2}}}$

$\displaystyle\\a=\sqrt{6-\sqrt{35}}-\sqrt{6+\sqrt{35}}=\left(\sqrt{\frac{7}{2}}-\sqrt{\frac{5}{2}}\right)-\left(\sqrt{\frac{7}{2}}+\sqrt{\frac{5}{2}}\right)=\\\\=\sqrt{\frac{7}{2}}-\sqrt{\frac{5}{2}}-\sqrt{\frac{7}{2}}-\sqrt{\frac{5}{2}}=\\\\=-\sqrt{\frac{5}{2}}-\sqrt{\frac{5}{2}}=-2\sqrt{\frac{5}{2}}=-\sqrt{\frac{4\times 5}{2}}=-\sqrt{2\times5}=-\sqrt{10}\\\\\boxed{\bf a=-\sqrt{10}}\\\\\Big(a+\sqrt{10}\Big)^{2007} = \Big(-\sqrt{10}+\sqrt{10}\Big)^{2007} =0^{2007} =\boxed{\bf 0}$