a+b=3,ab=-2,则(a+1)(b+1)=
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解决时间 2021-02-19 01:11
- 提问者网友：那叫心脏的地方装的都是你
- 2021-02-18 15:18
a+b=3,ab=-2,则(a+1)(b+1)=
最佳答案
- 五星知识达人网友：逃夭
- 2021-02-18 15:34
已知：a + b = 3； a b = -2
则(a+1)(b+1) = ab + a + b + 1 = ab + (a + b) + 1 = -2 + 3 + 1 = 2
补充：
1/a + 1/b = (a+b) / (ab) = 3 / (-2) = -3/2
a² + b² = (a+b)² - 2ab = 3² - 2(-2) = 13
a³ + b³ = (a+b)(a² - ab + b²) = (a+b) [(a+b)² - 3ab] = (a+b)³ - 3ab(a+b) = 27 + 6*3 = 45
a⁴+ b⁴=[a² + b²]² - 2a²b² = [(a + b)² - 2ab]² - 2a²b² = [9+4]² - 2*4 = 161
a - b = ±√(a - b)² = ±√[(a + b)² - 4ab] = ±√[9 +8] = ±√17
a² - b² = (a+b)*(a-b) = ±3√17
a³ - b³ = (a-b)(a² + ab + b²) = (a-b) [(a+b)² - ab] = ±11√17
则(a+1)(b+1) = ab + a + b + 1 = ab + (a + b) + 1 = -2 + 3 + 1 = 2
补充：
1/a + 1/b = (a+b) / (ab) = 3 / (-2) = -3/2
a² + b² = (a+b)² - 2ab = 3² - 2(-2) = 13
a³ + b³ = (a+b)(a² - ab + b²) = (a+b) [(a+b)² - 3ab] = (a+b)³ - 3ab(a+b) = 27 + 6*3 = 45
a⁴+ b⁴=[a² + b²]² - 2a²b² = [(a + b)² - 2ab]² - 2a²b² = [9+4]² - 2*4 = 161
a - b = ±√(a - b)² = ±√[(a + b)² - 4ab] = ±√[9 +8] = ±√17
a² - b² = (a+b)*(a-b) = ±3√17
a³ - b³ = (a-b)(a² + ab + b²) = (a-b) [(a+b)² - ab] = ±11√17
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