Question

Calculati folosind formulele de calcul prescurtat:
a) (3-√2)² ; (2-√3)² ; (4+√2)² ;
b) (4-√3)² ; (5-√2)² ; (√5+√3)² ;
c) (√5-√2)² ; (√5+√7)² ; (√3+2)² ;
d) (3-√5)² ; (√3-√2)² ; (√6+2)² ;
e) (√6-3)² ; (√5-√6)² ; (2√3-1)² ;
g) (√6-√3) (√6+√3)-(√6-√10) (√6+√10).
Va rog sa ma ajutati

Answer 1

Răspuns:

a)

(3-√2)² = 3² - 2×3×√2 + (√2)² = 9 - 6√2 + 2 = 11 - 6√2;

(2-√3)² = 2² - 2×2×√3 + (√3)² = 2 - 4√3 + 3 = 5 - 4√√3;

(4+√2)² = 4² + 2×4×√2 + (√2)² = 16 + 8√2 + 2 = 18 + 8√2;

b)

(4-√3)² = 4² - 2×4×√3 + √3² = 16 - 8√3 + 3 = 13 - 8√3;

(5-√2)² = 5² - 2×5×√2 + √2² = 25 - 10√2 + 2 = 27 - 10√2;

(√5+√3)² = √5² + 2×√5×√3 + √3² = 5 + 2√15 + 3 = 8 + 2√15;

c)

(√5-√2)² = √5² - 2×√5×√2 + √2² = 5 - 2√10 + 2 = 7 - 2√10;

(√5+√7)² = √5² + 2×√5×√7 + √7² = 5 + 2√35 + 7 = 12 + 2√35;

(√3+2)² = √3² + 2×√3×2 + 2² = 3 + 4√3 + 4 = 7 + 4√3;

d)

(3-√5)² = 3² - 2×3×√5 + √5² = 9 - 6√5 + 5 = 14 - 6√5;

(√3-√2)² = √3² - 2×√3×√2 + √2² = 3 - 2√6 + 2 = 5 - 2√6;

(√6+2)² = √6² + 2×√6×2 + 2² = 6 + 4√6 + 4 = 10 + 4√6;

e)

(√6-3)² = √6² - 2×√6×3 + 3² = 6 - 6√6 + 9 = 15 - 6√6;

(√5-√6)² = √5² - 2×√5×√6 + √6² = 5 - 2√30 + 6 = 11 - 2√30;

(2√3-1)² = (2√3)² - 2×2√3×1 + 1² = 4×3 - 4√3 + 1 = 12 - 4√3 + 1 = 13 - 4√3;

g)

(√6-√3) (√6+√3)-(√6-√10) (√6+√10) =

(√6² -√3²) (√6² - √10²) =

(6 - 3) (6 - 10) =

3 × (-4) =

- 12

Explicație pas cu pas:

formulele de calcul prescurtat sunt :

(a - b)² = a² - 2×a×b + b²

(a + b)² = a² + 2×a×b + b²

(a - b)(a + b) = a² - b²