若a-b=5,ab=-6,求:(1)a²+b².(2)a²-b².(3)a³+b³.
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若a-b=5,ab=-6,求:(1)a²+b².(2)a²-b².(3)a³+b³.
若a-b=5,ab=-6,求:(1)a²+b².(2)a²-b².(3)a³+b³.
若a-b=5,ab=-6,求:(1)a²+b².(2)a²-b².(3)a³+b³.
a-b=5,ab=-6
(1)a²+b²
=a²-2ab+b²+2ab
=(a-b)²+2ab
=5²+2×(-6)
=13
(2)(a+b)²
=a²+2ab+b²
=13-2×6
=1
∴a+b=±1
a²-b²
=(a+b)(a-b)
=±1×5
=±5
(3)a³+b³.
=(a+b)(a²-ab+b²)
=±1×﹙13+6)
=±19
a-b=5,ab=-6
(1)a²+b²
=a²-2ab+b²+2ab
=(a-b)²+2ab
=5²+2×(-6)
=13
(2)(a+b)²
=a²+2ab+b²
=13-2×6
=1
∴a+b=±1
a²-...
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a-b=5,ab=-6
(1)a²+b²
=a²-2ab+b²+2ab
=(a-b)²+2ab
=5²+2×(-6)
=13
(2)(a+b)²
=a²+2ab+b²
=13-2×6
=1
∴a+b=±1
a²-b²
=(a+b)(a-b)
=±1×5
=±5
(3)a³+b³.
=(a+b)(a²-ab+b²)
=±1×﹙13+6)
=±19
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(a-b)^2= a^2-2ab+b^2
a^2+b^2=(a-b)^2+2ab=5^2+2x(-6)=13
(a+b)^2=a^2+2ab+b^2=13+2x(-6)=1
a+b=1或-1
a^2-b^2=(a+b)(a-b)=5或-5
(a+b)³=a³+3a²b+3ab²+b³=a^3+b^3+3ab(a+b)
a^3+b^3=(a+b)³-3ab(a+b)=1^3-3*(-6)*1=19
或=(-1)^3-3*(-6)*(-1)=-19