Question

Va rog mult. Dau coroana

Answer 1

19. a)

a=3√3-2 si b=5-√6

a=√(3²×3)-2=√27-2=5,19-2=3,196

b= 5-√6=5-2,449=2,55

deci a>b

b)

$a=\sqrt{12}+\sqrt{27}+\sqrt{243}-\sqrt{432}$

$\sqrt{12}=\sqrt{3\cdot2^{2}}=2\sqrt{3} ;\sqrt{27} =\sqrt{3^{3}}=3\sqrt{3} ;\sqrt{243}=\sqrt{3^{5}} =9\sqrt{3} ;432=\sqrt{3^{3}\cdot2^{4}} =12\sqrt{3}$

$a=2\sqrt{3} +3\sqrt{3}+9\sqrt{3} -12\sqrt{3} =2\sqrt{3}$

$b=\sqrt{\sqrt{3}-2}+\sqrt{7+4\sqrt{3}}- \sqrt{19+8\sqrt{3}}$

$\sqrt{7+4\sqrt{3}}=\sqrt{\frac{7+\sqrt{49-48}}{2}}+\sqrt{\frac{7-\sqrt{49-48}}{2}}=\sqrt{4}+\sqrt{3} =2+\sqrt{3}$

$\sqrt{19+\sqrt{1536}}=\sqrt{\frac{19+\sqrt{361-1536}}{2}}+\sqrt{\frac{19-\sqrt{361-1536}}{2}}=$