calculeaza ( radical10 *radical90: radical50)^2-(radical90-radical40)^2
Răspunsuri la întrebare
(√(10*90:50))² - (3√10 - 2√10)² = (√18)² - (√10)² = 18 - 10 = 8 La prima paranteza am scris totul sub un radical si am efectuat calculele, iar la a doua paranteza am descompus √90 si √40, dupa care am efectuat calculele.
[tex] \displaystyle\\ \Big(\sqrt{10} \times \sqrt{90}: \sqrt{50}\Big)^2-\Big(\sqrt{90}-\sqrt{40}\Big)^2= \\\\ =\left(\frac{\sqrt{10} \times \sqrt{90}}{\sqrt{50}}\right)^2-\Big(\sqrt{90}-\sqrt{40}\Big)^2= \\\\ =\left(\frac{\sqrt{10} \times \sqrt{10} \times \sqrt{9}}{\sqrt{25\times2}}\right)^2-\Big(\sqrt{10} \times \sqrt{9}-\sqrt{10} \times \sqrt{4}\Big)^2= \\\\ =\left(\frac{10 \times 3}{5\sqrt{2}}\right)^2-\left(\sqrt{10}\Big(\sqrt{9}-\sqrt{4}\Big)\right)^2= [/tex]
[tex] \displaystyle\\ =\left(\frac{2 \times 3}{\sqrt{2}}\right)^2-\left(\sqrt{10}(3-2)\right)^2=\\\\ =\left(\frac{6}{\sqrt{2}}\right)^2-\left(\sqrt{10}\right)^2=\\\\ =\frac{36}{2}-10=18-10=\boxed{\bf 8} [/tex]