作业帮(1):若;2/(x^2-x+1)=1/x,求x^2/(x^4-1)的值.(2):y=√17－x,xy=3,求x^3+y
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(1):若;2/(x^2-x+1)=1/x,求x^2/(x^4-1)的值.(2):y=√17－x,xy=3,求x^3+y^3的值 两题求解,过程. 11 分钟
(1):若;2/(x^2-x+1)=1/x
2x/(x²-x+1)=1
2/(x-1+1/x)=1
x-1+1/x=2
x+1/x=3
x²+2+1/x²=9
x²+1/x²=7
(x-1/x)²=5
x-1/x=±√5
所以
x²/(x^4-1)
=1/(x²-1/x²)
=1/(x+1/x)(x-1/x)
=± 1/(3√5)=±√5/15
(2) x³+y³=(x+y)³-3xy(x+y)
=(√17)³-3√17*3
=17√17-9√17
=8√17
2x/(x²-x+1)=1
2/(x-1+1/x)=1
x-1+1/x=2
x+1/x=3
x²+2+1/x²=9
x²+1/x²=7
(x-1/x)²=5
x-1/x=±√5
所以
x²/(x^4-1)
=1/(x²-1/x²)
=1/(x+1/x)(x-1/x)
=± 1/(3√5)=±√5/15
(2) x³+y³=(x+y)³-3xy(x+y)
=(√17)³-3√17*3
=17√17-9√17
=8√17
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