已知ax+by=7,ax2+by2=49,ax3+by3=133,ax4+by4=406.求2003(x+y)+6xy-7/2(a+b)的值
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![已知ax+by=7,ax2+by2=49,ax3+by3=133,ax4+by4=406.求2003(x+y)+6xy-7/2(a+b)的值](/uploads/image/z/5408726-14-6.jpg?t=%E5%B7%B2%E7%9F%A5ax%2Bby%3D7%2Cax2%2Bby2%3D49%2Cax3%2Bby3%3D133%2Cax4%2Bby4%3D406.%E6%B1%822003%28x%2By%29%2B6xy-7%2F2%28a%2Bb%29%E7%9A%84%E5%80%BC)
已知ax+by=7,ax2+by2=49,ax3+by3=133,ax4+by4=406.求2003(x+y)+6xy-7/2(a+b)的值
已知ax+by=7,ax2+by2=49,ax3+by3=133,ax4+by4=406.求2003(x+y)+6xy-7/2(a+b)的值
已知ax+by=7,ax2+by2=49,ax3+by3=133,ax4+by4=406.求2003(x+y)+6xy-7/2(a+b)的值
ax + by = 7,两边同时乘以x + y,由ax2+by2=49,得到49 + (a + b)xy = 7(x + y) ***
ax2+by2=49,两边同时乘以x + y,由ax3+by3=133,得到19 + xy = 7(x + y) *
ax3+by3=133,两边同时乘以x + y,由ax4+by4=406,得到58 + 7xy = 19(x + y) **
解* 和 ** 式子,得到 xy = -1.5,x + y = 2.5
带入***式子,得到a + b = 21,
最后结果可得.
已知ax+by=7,ax²+by²=49,ax³+by³=133,ax⁴+by⁴=406,求2003(x+y)+6xy-(7/2)(a+b)的值
(ax+by)(x+y)=ax²+by²+(a+b)xy=49+(a+b)xy=7(x+y)
即有(a+b)xy-7(x+y)=-49.............
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已知ax+by=7,ax²+by²=49,ax³+by³=133,ax⁴+by⁴=406,求2003(x+y)+6xy-(7/2)(a+b)的值
(ax+by)(x+y)=ax²+by²+(a+b)xy=49+(a+b)xy=7(x+y)
即有(a+b)xy-7(x+y)=-49.............(1)
(ax²+by²)(x+y)=ax³+by³+xy(ax+by)=133+7xy=49(x+y)
即有7xy-49(x+y)=-133..............(2)
(ax³+by³)(x+y)=ax⁴+by⁴+xy(ax²+by²)=406+49xy=133(x+y)
即有49xy-133(x+y)=-406...........(3)
7×(2)-(3)得 x+y=525/210=105/42=5/2;7xy-49(5/2)=-133,故xy=-3/2;
将xy和x+y之值代入(1)式即得a+b=21
于是2003(x+y)+6xy-(7/2)(a+b)=2003×(5/2)+6×(-3/2)-(7/2)×21=(10015-18-147)/2=4925
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