ZADANIE 20
Odpowiedź:
(√3)² = 3
³√3³ = ³√27 = 3
√(-3)² = √9 =3
(³√3)³ = 3
(- ³√3)³ = - 3
√√(-3)⁴ =√√81 = √9 = 3
√(3√(-3)²) = √3(√9) = √3*3 = √9 = 3
Odp. Liczba (- ³√3)³ nie jest równa pozostałym bo wynosi (-3)
ZAD 21
a) √5 (3 - √5) = 3√5 - (√5)² = 3√5 - 5 = - (5 - 3√5)
b) √2 (5√2 - 3) = 5 (√2)² - 3 √2 = 5 * 2 - 3√2 = 10 - 3√2
c) - √3(2√3 + 5) = - 2 (√3)² - 5√3 = - 2 * 3 - 5√3 = - 6 - 5√3 = - (6 + 5√3)
d) 2√7 (4 + √7) = 8√7 + 2 (√7)² = 8√7 + 14 = 2 (7 + 4√7)
e) 3√5 (3 - 2√5) = 9√5 - 6 (√5)² = 9√5 - 30 = - 3 (10 - 3√5)
f) - 4√2(3√2 - 1) = - 12 (√2)² + 4√2 = - 24 + 4√2 = - 4 (6 - √2)
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ZADANIE 20
Odpowiedź:
(√3)² = 3
³√3³ = ³√27 = 3
√(-3)² = √9 =3
(³√3)³ = 3
(- ³√3)³ = - 3
√√(-3)⁴ =√√81 = √9 = 3
√(3√(-3)²) = √3(√9) = √3*3 = √9 = 3
Odp. Liczba (- ³√3)³ nie jest równa pozostałym bo wynosi (-3)
ZAD 21
a) √5 (3 - √5) = 3√5 - (√5)² = 3√5 - 5 = - (5 - 3√5)
b) √2 (5√2 - 3) = 5 (√2)² - 3 √2 = 5 * 2 - 3√2 = 10 - 3√2
c) - √3(2√3 + 5) = - 2 (√3)² - 5√3 = - 2 * 3 - 5√3 = - 6 - 5√3 = - (6 + 5√3)
d) 2√7 (4 + √7) = 8√7 + 2 (√7)² = 8√7 + 14 = 2 (7 + 4√7)
e) 3√5 (3 - 2√5) = 9√5 - 6 (√5)² = 9√5 - 30 = - 3 (10 - 3√5)
f) - 4√2(3√2 - 1) = - 12 (√2)² + 4√2 = - 24 + 4√2 = - 4 (6 - √2)