已知x+y=6,xy=7,求值:1.x²+y²,2.x²-xy+y² 3.x
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已知x+y=6,xy=7,求值:1.x²+y²,2.x²-xy+y² 3.x²y+xy² 4.x-y
上面的平方可能会变成2,所以重新打了一遍..
上面的平方可能会变成2,所以重新打了一遍..
x²+y²
= x²+y²+2xy-2xy
= (x+y)² -2xy
= 6²-2×7
= 36-14
= 22
x²-xy+y²
= x²+y²+2xy-3xy
= (x+y)² -3xy
= 6² -3×7
= 36-21
= 15
x²y+xy²
= xy(x+y)
= 7×6
= 42
因为 x+y=6,xy=7,可得 x,y都是正数
又 (x-y)² = (x+y)² -4xy = 6²-4×7 = 36-28 = 8
所以 x-y = √8 = 2√2
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= x²+y²+2xy-2xy
= (x+y)² -2xy
= 6²-2×7
= 36-14
= 22
x²-xy+y²
= x²+y²+2xy-3xy
= (x+y)² -3xy
= 6² -3×7
= 36-21
= 15
x²y+xy²
= xy(x+y)
= 7×6
= 42
因为 x+y=6,xy=7,可得 x,y都是正数
又 (x-y)² = (x+y)² -4xy = 6²-4×7 = 36-28 = 8
所以 x-y = √8 = 2√2
--------------------
梳理知识,帮助别人,愉悦自己.
“数理无限”团队欢迎你
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