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中四聯合方程
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有沒有可以話比我知呢兩條數點計? 要有step! 1. CE 2004/ll/42 If α≠β and { α^2 = 4α+3 { β^2 = 4β+3, then (α+1)β+1) = ? 2. CE 2001/ll/39 If a, b are distinct real number and { a^2+4a+1 = 0 { b^2+4b+1 = 0, find a^2+b^2
畀心機呀！！！☆ヾ(???)ノ 你問得好有條理，好清楚！ 1. CE 2004/ll/42 If α ≠ β and { α2 = 4α + 3 { β2 = 4β + 3, then (α+1)(β+1) = ? From the given information, α and β are two distinct roots of the quadratic equation x2 = 4x + 3, or x2 - 4x - 3 = 0. Sum of roots = α + β = -(-4)/1 = 4 Product of roots = αβ = -3/1 = -3 Consider (α+1)(β+1) = αβ + α + β + 1 = -3 + 4 + 1 = 2 2. CE 2001/ll/39 If a, b are distinct real number and { a2 + 4a + 1 = 0 { b2 + 4b + 1 = 0, find a2 + b2. From the given information, a and b are two distinct real roots of x2 + 4x + 1 = 0 Sum of roots = a + b = -4 Product of roots = ab = 1 Consider a2 + b2 = a2 + 2ab + b2 - 2ab = (a + b)2 - 2ab = (-4)2 - 2(1) = 14
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中四聯合方程
發問:
有沒有可以話比我知呢兩條數點計? 要有step! 1. CE 2004/ll/42 If α≠β and { α^2 = 4α+3 { β^2 = 4β+3, then (α+1)β+1) = ? 2. CE 2001/ll/39 If a, b are distinct real number and { a^2+4a+1 = 0 { b^2+4b+1 = 0, find a^2+b^2
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最佳解答:畀心機呀！！！☆ヾ(???)ノ 你問得好有條理，好清楚！ 1. CE 2004/ll/42 If α ≠ β and { α2 = 4α + 3 { β2 = 4β + 3, then (α+1)(β+1) = ? From the given information, α and β are two distinct roots of the quadratic equation x2 = 4x + 3, or x2 - 4x - 3 = 0. Sum of roots = α + β = -(-4)/1 = 4 Product of roots = αβ = -3/1 = -3 Consider (α+1)(β+1) = αβ + α + β + 1 = -3 + 4 + 1 = 2 2. CE 2001/ll/39 If a, b are distinct real number and { a2 + 4a + 1 = 0 { b2 + 4b + 1 = 0, find a2 + b2. From the given information, a and b are two distinct real roots of x2 + 4x + 1 = 0 Sum of roots = a + b = -4 Product of roots = ab = 1 Consider a2 + b2 = a2 + 2ab + b2 - 2ab = (a + b)2 - 2ab = (-4)2 - 2(1) = 14
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