(1)已知:x+y=5,x눀+y눀=13,求代数式x대y+2x눀y눀+xy대的值

2025-01-04 02:36:17
推荐回答(3个)
回答1:

(1)x³y+2x²y²+xy³=xy(x^2+2xy+y^2)=xy*(x+y)^2
而(x+y)^2=25,x²+y²=13,xy=6
所以xy*(x+y)^2=150
(2)a²b+ab²=ab(a+b)=40*13=520
(3)202²-54²+256×352
=(202+54)*(202-54)+256×352
=256*148+256×352
=256*500
=128000
(4)|x+2y-1|+(2x-y-2)² =0
则x+2y=1
2x-y=2
(2x-y)² -2(2x-y)+(x+2y)²
=2^2-2*2+1^2
=1

回答2:

(1)由x+y=5得:(x+y)² =25,所以x²+y²+2xy=25,所以xy=6
代数式x³y+2x²y²+xy³=xy(x+y)² =6×25=150
(2)a²b+ab²=ab(a+b)=40×13=520
(3)202²-54²+256×352=(202+54)×(202-54)+256×352=256×148+256×352
=256×(148+352)=256×500=128000
(4)由已知得:x+2y-1=0且2x-y-2=0,所以x=1,y=0
所以(2x-y)² -2(2x-y)+(x+2y)² =4-2×2+1=1

回答3:

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