Question

Вычислите: а) 6²- 5² + 3² - 2² б) (8² : 16 - 2)² + 2³ ! !

Answer 1

А) 6²- 5² + 3² - 2²= 36 - 25 + 9 - 4 = 16

▪или так применив формулу: a²- b² = (a - b)(a + b)

6²- 5² + 3² - 2²= (6²- 5²) + (3² - 2²)=(6-5)(6+5) + (3-2)(3+2) = 1×11 + 1×5 = 11 + 5 = 16

б) (8² : 16 - 2)² + 2³ = (64 : 16 - 2)² + 2³ = (4 - 2)² + 2³ = 2² + 2³ = 4 + 8 = 12

▪или так применив формулы:
${a}^{m} \div {a}^{n} = {a}^{m - n} \\ ( {a}^{m} ) ^{n} = {a}^{m \times n}$
${8}^{2} \div 16 = {( {2}^{3}) }^{2} \div {2}^{4} = {2}^{6} \div {2}^{4} = {2}^{2} = 4$
(a - b)² = а² - 2аb + b² т.е.
(4 - 2)² = 4² -2аb + 2² = 16 - 2×4×2 + 4 = 16 - 16 + 4 = 4

(8² : 16 - 2)² + 2³ = (4 - 2)²+ 2³ = 4 + 2³ = 4 + 8 = 12