x+1/4=3,则代数式x²+1/x²的值是?请给出解题过程,打错了是X+1/x=3
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![x+1/4=3,则代数式x²+1/x²的值是?请给出解题过程,打错了是X+1/x=3](/uploads/image/z/3819564-36-4.jpg?t=x%2B1%2F4%3D3%2C%E5%88%99%E4%BB%A3%E6%95%B0%E5%BC%8Fx%26%23178%3B%2B1%2Fx%26%23178%3B%E7%9A%84%E5%80%BC%E6%98%AF%3F%E8%AF%B7%E7%BB%99%E5%87%BA%E8%A7%A3%E9%A2%98%E8%BF%87%E7%A8%8B%2C%E6%89%93%E9%94%99%E4%BA%86%E6%98%AFX%2B1%2Fx%3D3)
x+1/4=3,则代数式x²+1/x²的值是?请给出解题过程,打错了是X+1/x=3
x+1/4=3,则代数式x²+1/x²的值是?请给出解题过程,
打错了是X+1/x=3
x+1/4=3,则代数式x²+1/x²的值是?请给出解题过程,打错了是X+1/x=3
x+1/x=3
两边平方
x²+2*x*1/x+1/x²=9
x²+2+1/x²=9
x²+1/x²=7
x+1/x=3, (x+1/x)²=x²+1/x²+2
x²+1/x²= (x+1/x)²-2 =9-2=7
x+1/4=3 x=11/4 x²+1/x²=15125/484
呃,x=3-1/4=2.75 x²+1/x²=2.75²+1/2.75²=7.5625+1/7.5625=7.6947
x=3-1/4=11/4
x^2+1/x^2=121/16+16/121=14897/1936
(x+1)/4=3,x=11,代入,=1+1/121
由题意得:
(1)x+1/4=3
x=3-1/4=11/4
(2) 将x=11/4代入x²+1/x²=14897/1936