第(1)题、第7题的第(3)题
来源:学生作业帮 编辑:搜搜考试网作业帮 分类:数学作业 时间:2024/08/18 04:20:15
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第(1)题、第7题的第(3)题
![第(1)题、第7题的第(3)题](/uploads/image/z/18095321-65-1.jpg?t=%E7%AC%AC%EF%BC%881%EF%BC%89%E9%A2%98%E3%80%81%E7%AC%AC7%E9%A2%98%E7%9A%84%E7%AC%AC%EF%BC%883%EF%BC%89%E9%A2%98)
第(1)题,
(a^2+1/a^2)²
=a^4+1/a^4+2
=49,
a^4+1/a^4=47
第7题
xy-y²=y(x-y)=y(√x-√y)(√x+√y),
x√x-y√y=(√x-√y)(x+√(xy)+√y),【a³-b³=(a-b)(a²+b²+ab)】
因此,﹙x√x﹢x√y)/(xy﹣y²﹚﹣﹙x﹢√xy﹢y)/(x√x﹣y√y﹚
=x/[y(√x-√y)]-1/(√x-√y)
=(x/y-1)/(√x-√y)
=(1/y)*(x-y)/(√x-√y)
=(√x+√y)/y
(a^2+1/a^2)²
=a^4+1/a^4+2
=49,
a^4+1/a^4=47
第7题
xy-y²=y(x-y)=y(√x-√y)(√x+√y),
x√x-y√y=(√x-√y)(x+√(xy)+√y),【a³-b³=(a-b)(a²+b²+ab)】
因此,﹙x√x﹢x√y)/(xy﹣y²﹚﹣﹙x﹢√xy﹢y)/(x√x﹣y√y﹚
=x/[y(√x-√y)]-1/(√x-√y)
=(x/y-1)/(√x-√y)
=(1/y)*(x-y)/(√x-√y)
=(√x+√y)/y