Toán Lớp 9: cho :a=( \sqrt(2)-1)/2
và b=( \sqrt(2)+1)/2
tính A=a^7+b^7
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Toán Lớp 9: cho :a=( \sqrt(2)-1)/2
và b=( \sqrt(2)+1)/2
tính A=a^7+b^7
Comments ( 2 )
=> a = (√2 – 1)/2 = (-1 + √2)/2
=> a+b = -1; ab = (-1-√2)(-1+√2)/4 = -1/4
=> a²+b² = (a+b)² – 2ab = 1+1/2 = 3/2
=> a³+b³ = (a+b)³ – 3ab(a+b) = -1 – 3/4 = -7/4
=> a^4+b^4 = (a²+b²)² – 2a²b² = 9/4 – 1/8 = 17/8
=> a^7+b^7
= (a^4+b^4)(a³+b³) – a^4.b³ – a³.b^4
= (a^4+b^4)(a³+b³) – a³b³(a+b)
= (17/8)(-7/4) – (-1/4)³.(-1) = -239/64
<=> a = (√2 – 1)/2 = (-1 + √2)/2
<=> a+b = -1; ab = (-1-√2)(-1+√2)/4 = -1/4
<=> a²+b² = (a+b)² – 2ab = 1+1/2 = 3/2
<=> a³+b³ = (a+b)³ – 3ab(a+b) = -1 – 3/4 = -7/4
<=> a^4+b^4 = (a²+b²)² – 2a²b² = 9/4 – 1/8 = 17/8
<=> a^7+b^7
<=>(a^4+b^4)(a³+b³) – a^4.b³ – a³.b^4
<=> (a^4+b^4)(a³+b³) – a³b³(a+b)
<=>(17/8)(-7/4) – (-1/4)³.(-1)