Question

4. Calculaţi: Foloseste formula de calcul prescurtat. a) 4(3√3-1)² -5(√3-4)²-√768; b) 3(2√2+1)² +2(√2-3)²-(8-√7)(8+√7); c) 6(√2+3)²+4(3√2-1)²-√288; d) (√6+2)²+(√3-2√2)²-(√10-√3)(√10+√3); e) (√7-2)² +2(√7+1)²+(√7-3)(√7+3). Dau coroana doar daca raspunsul foloseste formula de calcul prescurtat.​

Answer 1

Răspuns:

Explicație pas cu pas:

(a±b)²=a²±2ab+b²

(a-b)(a+b)=a²-b²

a.  4(3√3-1)² -5(√3-4)²-√768

4(27-6√3+1)-5(3-8√3+16)-16√3=

112-24√3-95+40√3-16√3=17

b.  3(2√2+1)² +2(√2-3)²-(8-√7)(8+√7)=

3(8+4√2+1)+2(2-6√2+9)-(64-7)=

27+12√2+22-12√2-57=-8

c.  6(√2+3)²+4(3√2-1)²-√288=

6(2+6√2+9)+4(18-6√2+1)-12√2=

66+36√2+76-24√2-12√2=142

d.   (√6+2)²+(√3-2√2)²-(√10-√3)(√10+√3)=

6+4√6+4+3-4√6+8-10+3=11

e.   (√7-2)² +2(√7+1)²+(√7-3)(√7+3)=

7-4√7+4+2(7+2√7+1)+7-9=

7-4√7+16+4√7-2=21