Question

tot exercitiul va rog

Answer 1

Răspuns

a. √2

b.   3

c.   1  

Explicație pas cu pas:

a.[1\(6+√5)+1\(√5+√4)+1\(√4+√3)+1\(√3+√2)]\(√3-1)=

[(√6-√5)\(6-5)+(√5-√4)\5-4+(√4-√3)\4-3+(√3-√2)\3-2]\(√3-1)=

[(√6-√5)\1+(√5-√4)\1+(√4-√3)\1+(√3-√2)\1]*1\(√3-1)=

(√6-√5+√5-√4+√4-√3+√3-√2)\1*1\(√3-1)=

(√6-√√2)\(√3-1)=

(√6-√2)\(√3-1)=(√3+1)(√6-√2)\(3-1)=(√18+√6-√6-√2)\2=

(√18+√6-√6-√2)2=(3√2-√2)\2=

√2(3-1)\2=2√2\2=√2

b..   [6\(3√2+2√3)+3\(2√3+3)]\(√2-1)=

[6(3√2-2√3)\(9*2)-(4*3)+3(2√3-3)\(4*3-9)]\(√2-1)=

[(18√2-12√3)\(18-12)+(6√3-9)\(12-9)*1\(√2-1)=

[(18√2-12√3)\\6+(6√3-9)\3]*1\(√2-1)=

18√2-12√3+12√3-18)\6*1\(√2-1)=

(18√2-18)\6*1\(√2-1)=18(√√2-1)\6(√2-1)=18\6=3

c.   [5\(√8+√3)+2\(√3+1)]\[√6\√3+√10\√5-√8\2√2]=

5(√8-√3)\(8-3)+2(√3+1)\(3-1]\[(√6*√3)\3+(√5*√10)\5-(√8*2√2)\4*2]=

[(5√8-5√3)√\5+(2√3+2)\2]\[√18\3+√50\5-2√16\8]=

[2(5√8-5√3)+5(2√3+2)]\10\[(40√18√+24√50-30√16)\120]=

[(10√8-10√3+10√3+10)\10]\[(40*3√2+24*5√2-30*4)\120=

[(10√8+10)\10]\10\[(120√2+120√2-120)\120=[10(8+1)\10]\[(120(√2+√2-1)\120]=

[(2√2+1)\2√2-1)=2(2√2-1)(2√2+1)]\(4*2-1)=(4*2-1)\(4*2-1)=7\7=1