几道数学题填空a+1/a=3,那么a^2+1/a^2的值_________计算(1) (-8)^2002*(-0.125
1个回答
1.
a+1/a=3
(a+1/a)^2=9
a^2+2+1/a^2=9
a^2+1/a^2=7
(1)
(-8)^2002*(-0.125)^2003
=(-8)^2002*(-0.125)^2002*(-0.125)
=(8*0.125)^2002*(-0.125)
=1^2002*(-0.125)
=-0.125
(2)
[(a^2+2ab+b^2)-a(a^2-b^2)]/(a+b)
=[(a+b)^2-a(a+b)(a-b)]/(a+b)
=(a+b)-a(a-b)
=a+b-a^2+ab
(3)
x^2+x-1=0
x^2+x=1
x^3+2x^2+3
=x(x^2+x)+x^2+3
=x+x^2+3
=1+3
=4
(4)
x^2+3xy+y^2
=(x-y)^2+5xy
=9+5*9
=54
(5)
100^2-99^2+98^2-97^2+96^2-95^2+…+2^2-1
=(100+99)(100-99)+(98+97)(98-97)+(96+95)(96-95)+…+(2+1)(2-1)
=100+99+98+98+96+95+…+2+1
=5050
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