恒等变形题(35)例1:若 X^2-8x+13=0,求 :(X^4-6X^3-2X^2+18X+23)/(X^2-8X+15)的值.例2:若 X^2-3X+1=0,求:(2X^5-5X^4+2X^3-8X^2)/(X^2+1)的值.【这两题我化不出,】劳驾!
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![恒等变形题(35)例1:若 X^2-8x+13=0,求 :(X^4-6X^3-2X^2+18X+23)/(X^2-8X+15)的值.例2:若 X^2-3X+1=0,求:(2X^5-5X^4+2X^3-8X^2)/(X^2+1)的值.【这两题我化不出,】劳驾!](/uploads/image/z/6898585-49-5.jpg?t=%E6%81%92%E7%AD%89%E5%8F%98%E5%BD%A2%E9%A2%98%EF%BC%8835%EF%BC%89%E4%BE%8B1%EF%BC%9A%E8%8B%A5+X%5E2%EF%BC%8D8x%EF%BC%8B13%EF%BC%9D0%2C%E6%B1%82+%EF%BC%9A%EF%BC%88X%5E4%EF%BC%8D6X%5E3%EF%BC%8D2X%5E2%EF%BC%8B18X%EF%BC%8B23%EF%BC%89%EF%BC%8F%EF%BC%88X%5E2%EF%BC%8D8X%EF%BC%8B15%EF%BC%89%E7%9A%84%E5%80%BC.%E4%BE%8B2%EF%BC%9A%E8%8B%A5+X%5E2%EF%BC%8D3X%EF%BC%8B1%EF%BC%9D0%2C%E6%B1%82%EF%BC%9A%EF%BC%882X%5E5%EF%BC%8D5X%5E4%EF%BC%8B2X%5E3%EF%BC%8D8X%5E2%EF%BC%89%EF%BC%8F%EF%BC%88X%5E2%EF%BC%8B1%EF%BC%89%E7%9A%84%E5%80%BC.%E3%80%90%E8%BF%99%E4%B8%A4%E9%A2%98%E6%88%91%E5%8C%96%E4%B8%8D%E5%87%BA%2C%E3%80%91%E5%8A%B3%E9%A9%BE%21)
恒等变形题(35)例1:若 X^2-8x+13=0,求 :(X^4-6X^3-2X^2+18X+23)/(X^2-8X+15)的值.例2:若 X^2-3X+1=0,求:(2X^5-5X^4+2X^3-8X^2)/(X^2+1)的值.【这两题我化不出,】劳驾!
恒等变形题(35)
例1:若 X^2-8x+13=0,求 :(X^4-6X^3-2X^2+18X+23)/(X^2-8X+15)的值.例2:若 X^2-3X+1=0,求:(2X^5-5X^4+2X^3-8X^2)/(X^2+1)的值.【这两题我化不出,】劳驾!
恒等变形题(35)例1:若 X^2-8x+13=0,求 :(X^4-6X^3-2X^2+18X+23)/(X^2-8X+15)的值.例2:若 X^2-3X+1=0,求:(2X^5-5X^4+2X^3-8X^2)/(X^2+1)的值.【这两题我化不出,】劳驾!
(1)分子X^4-6X^3-2X^2+18X+23 同时加减2x^2
=X^4-8X^3+2x^3-2X^2+18X+23 前两项提取x^2
=x^2(x^2-8x)+2x^3-2X^2+18X+23 注意到括号里的值就是-13
=2x^3-15x^2+18X+23 同时加减x^2
=2x^3-16x^2+x^2+18X+23 前两项提取2x
=2x(x^2-8x) +x^2+18X+23 注意到括号里的值就是-13
=x^2-8x+23
=10
分母=X^2-8X+15=2
所以它的值是10/2=5
(2)分子2X^5-5X^4+2X^3-8X^2 同时加减X^4
=2X^5-6X^4+X^4+2X^3-8X^2 前两项提取2X^3
=2x^3(x^2-3x)+X^4+2X^3-8X^2 括号里的值是-1
=x^4-8x^2 注意到x^2就是3x-1带入化简
=9x^2-30x-9 注意到x^2就是3x-1带入化简
=-3x
分母=3x
所以它的值就是-1