Kadar+Adrian

Tema Matematica Optional

 1.Calculati valoarea expresiei //a² + b² + 2(ab + a + b)// ,stiind ca a + b =5. a² + b² + 2(ab + a + b) = a² + b² + 2ab + 2a + 2b (a + b)² + 2(a+b)  (a + b)(a+b + 2) =5 · (5+2)= 5 · 7 = 35 2.Calculati:  (√2 + √50 - √72) √2 + 8/21 : (-4/63) = (√2 + 5 √2 - 6 √2) √2 + 6 =2 + 6=  8 3.Aratati ca nr. 2001 + 2( 1 + 2 + 3 +…..+ 2000) nu e patrat perfect.2001 + 2(1 + 2 + 3 +….+2000) = 2001 + 2(2000· 2001) :2 =2001(1+2000) 2001² => este patrat pefect 4. Ip: ABCDA`B`C`D` - paralelipiped dreptunghic Concl: AA` || CC` A`C si AC` - concurente A`C` si BB` - necoplanareDem: ABB`A` - Paralelogram => AA` || BB`BCC`B` - Paralelogram => BB` || CC` (din ambele)=> BB`|| CC` ABCD – Paralelogram => [DC] || Ξ [AB] ABB`A` - Paralelogram => [A`B`] || Ξ [AB] (din ambele) => [DC] || Ξ [A`B`] => DCA`B` - Paralelogram => A`C si AC` =diagonale=>concurente A`, C € (A`B`D`)=> A`C ⊂ (A`B`D`) (1) B, B` € (BB`C) => BB` ⊂ (BB`C) (2) A` nu€ (BB`C) (3) Din (1), (2) si (3) => A`C` si BB` - necoplanare



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