Question

3 si 4 va rog mult de tot dau coroana

Answer 1

 

$\displaystyle\bf\\3)\\Stim~ca:\\x+y=-7\\y+z=1\\\\Se~cere:\\\\a)\\3x+3y-1=\\=3(x+y)-1=\\=3\times(-7)-1=\\=-21-1=\boxed{\bf-22}\\\\b)\\x+2y+z=\\=x+y+y+z=\\=(x+y)+(y+z)=\\=-7+1=\boxed{\bf-6}\\\\c)\\2x+5y+3z-7=\\=(2x+2y)+(3y+3z)-7=\\=2(x+y)+3(y+z)-7=\\=2\times(-7)+3\times1-7=-14+3-7=-11-7=\boxed{\bf-18}$

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$\displaystyle\bf\\4)~~Determinati~semnele~numerelor.\\\\a)~~(-3)\cdot(-6)\cdot(-9)\cdot\hdots\cdot(-2020)\\\\Avem~un~produs~de~multipli~ai~lui~3~scrisi~in~ordine~crescatoare.\\Observam~ca~ultimul~termen~(-2020)~nu~este~multiplu~al~lui~3.\\\\\implies~Greseala~de~tipar.\\Consider~ca~trebuia~scris~(-2019)~ca~la~punctul~b)$

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$\displaystyle\bf\\Rezolvare:\\\\a)~~(-3)\cdot(-6)\cdot(-9)\cdot\hdots\cdot(-2019)\\\\Calculam~numarul~de~factori~(Facem~abstractie~de~semnul~minus.)\\\\n=\frac{2019-3}{3}+1=\frac{2016}{3}+1=672+1=673~de~factori\\\\673~este~numar~impar\\\\Produsul~dintre~un~numar~impar~de~numere~negative\\are~rezultatul~negativ.\\\boxed{\bf\implies~Produsul~de~la~a)~are~semnul~minus.}$

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$\displaystyle\bf\\Rezolvare:\\\\a)~~(-3)\cdot(-6)\cdot(-9)\cdot\hdots\cdot(-2019)\\\\Calculam~numarul~de~factori~(Facem~abstractie~de~semnul~minus.)\\\\n=\frac{2019-3}{3}+1=\frac{2016}{3}+1=672+1=673~de~factori\\\\673~este~numar~impar\\\\Produsul~dintre~un~numar~impar~de~numere~negative\\are~rezultatul~negativ.\\\boxed{\bf\implies~Produsul~de~la~a)~are~semnul~minus.}$

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$\displaystyle\bf\\b)~~(-1)\cdot(-2)\cdot(-3)\cdot\hdots\cdot(-2019)\\\\De~la~1~la~2019~avem~2019~factori.\\2019~este~numar~impar.\\\\Produsul~dintre~un~numar~impar~de~numere~negative\\are~rezultatul~negativ.\\\boxed{\bf\implies~Produsul~de~la~b)~are~semnul~minus.}$