急!高一数学必修一人教A版第60页习题2.1B组第二题已知x+(x^-1)=3,求下列各数的值:(x^1/2)+(x^-1/2)=? (x^2)+(x^-2)=? (x^2)-(x^-2)=?答案我知道,但是我不会做,求各位帮帮忙……
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![急!高一数学必修一人教A版第60页习题2.1B组第二题已知x+(x^-1)=3,求下列各数的值:(x^1/2)+(x^-1/2)=? (x^2)+(x^-2)=? (x^2)-(x^-2)=?答案我知道,但是我不会做,求各位帮帮忙……](/uploads/image/z/227178-18-8.jpg?t=%E6%80%A5%21%E9%AB%98%E4%B8%80%E6%95%B0%E5%AD%A6%E5%BF%85%E4%BF%AE%E4%B8%80%E4%BA%BA%E6%95%99A%E7%89%88%E7%AC%AC60%E9%A1%B5%E4%B9%A0%E9%A2%982.1B%E7%BB%84%E7%AC%AC%E4%BA%8C%E9%A2%98%E5%B7%B2%E7%9F%A5x%2B%EF%BC%88x%5E-1%EF%BC%89%3D3%2C%E6%B1%82%E4%B8%8B%E5%88%97%E5%90%84%E6%95%B0%E7%9A%84%E5%80%BC%EF%BC%9A%28x%5E1%2F2%29%2B%28x%5E-1%2F2%29%3D%3F+++++%28x%5E2%29%2B%28x%5E-2%29%3D%3F++++%28x%5E2%29-%28x%5E-2%29%3D%3F%E7%AD%94%E6%A1%88%E6%88%91%E7%9F%A5%E9%81%93%2C%E4%BD%86%E6%98%AF%E6%88%91%E4%B8%8D%E4%BC%9A%E5%81%9A%2C%E6%B1%82%E5%90%84%E4%BD%8D%E5%B8%AE%E5%B8%AE%E5%BF%99%E2%80%A6%E2%80%A6)
急!高一数学必修一人教A版第60页习题2.1B组第二题已知x+(x^-1)=3,求下列各数的值:(x^1/2)+(x^-1/2)=? (x^2)+(x^-2)=? (x^2)-(x^-2)=?答案我知道,但是我不会做,求各位帮帮忙……
急!高一数学必修一人教A版第60页习题2.1B组第二题
已知x+(x^-1)=3,求下列各数的值:
(x^1/2)+(x^-1/2)=? (x^2)+(x^-2)=? (x^2)-(x^-2)=?
答案我知道,但是我不会做,求各位帮帮忙……
急!高一数学必修一人教A版第60页习题2.1B组第二题已知x+(x^-1)=3,求下列各数的值:(x^1/2)+(x^-1/2)=? (x^2)+(x^-2)=? (x^2)-(x^-2)=?答案我知道,但是我不会做,求各位帮帮忙……
1.因为[(x^1/2)+(x^-1/2)]^2
=x+(x^-1)+2
=3+2
=5,
且(x^1/2)+(x^-1/2)>0,
所以(x^1/2)+(x^-1/2)=根号5;
2.因为[x+(x^-1)]^2
=(x^2)+(x^-2)+2
=3^2=9,
所以(x^2)+(x^-2)=7;
3.因为[x-(x^-1)]^2
=(x^2)+(x^-2)-2
=7-2=5,
所以x-(x^-1)=根号5或-根号5,
所以(x^2)-(x^-2)
=[x+(x^-1)][x-(x^-1)],
因为x+(x^-1)=3,x-(x^-1)=根号5或-根号5,
所以(x^2)+(x^-2)=3根号5或-3根号5.
[(x^1/2)+(x^-1/2)]^2=x+(x^-1)+2=3+2=5
所以(x^1/2)+(x^-1/2)=根号5
(x^2)+(x^-2)=[x+(x^-1)]^2-2=7
(x^2)-(x^-2)=( x+x^-1)(x-x^-1)=3(x-x^-1)