已知关于X的方程(a²+3a+2)X²+(a+1)X+1/4=0总有实数根求a=-3时,8X1³+8X2²-X2的值(X1,X2是方程的两根,请用韦达定理)
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![已知关于X的方程(a²+3a+2)X²+(a+1)X+1/4=0总有实数根求a=-3时,8X1³+8X2²-X2的值(X1,X2是方程的两根,请用韦达定理)](/uploads/image/z/1268154-18-4.jpg?t=%E5%B7%B2%E7%9F%A5%E5%85%B3%E4%BA%8EX%E7%9A%84%E6%96%B9%E7%A8%8B%28a%26%23178%3B%2B3a%2B2%29X%26%23178%3B%2B%28a%2B1%29X%2B1%2F4%3D0%E6%80%BB%E6%9C%89%E5%AE%9E%E6%95%B0%E6%A0%B9%E6%B1%82a%3D-3%E6%97%B6%EF%BC%8C8X1%26%23179%3B%2B8X2%26%23178%3B-X2%E7%9A%84%E5%80%BC%EF%BC%88X1%2CX2%E6%98%AF%E6%96%B9%E7%A8%8B%E7%9A%84%E4%B8%A4%E6%A0%B9%EF%BC%8C%E8%AF%B7%E7%94%A8%E9%9F%A6%E8%BE%BE%E5%AE%9A%E7%90%86%EF%BC%89)
已知关于X的方程(a²+3a+2)X²+(a+1)X+1/4=0总有实数根求a=-3时,8X1³+8X2²-X2的值(X1,X2是方程的两根,请用韦达定理)
已知关于X的方程(a²+3a+2)X²+(a+1)X+1/4=0总有实数根
求a=-3时,8X1³+8X2²-X2的值(X1,X2是方程的两根,请用韦达定理)
已知关于X的方程(a²+3a+2)X²+(a+1)X+1/4=0总有实数根求a=-3时,8X1³+8X2²-X2的值(X1,X2是方程的两根,请用韦达定理)
当a=-3时
方程变为2X²-2X+1/4=0 8x²-8x+1=0总有实数根x1, x2
则8x1²-8x1+1=0 8x2²-8x2+1=0
所以8x1²=8x1-1 8x2²=8x2-1
则由韦达定理 x1+x2=1 x1*x2=1/8
所以8X1³+8X2²-X2=x1*(8x1-1))+8x2-1-x2
=8x1²-x1+7x2-1
=8x1-1-x1+7x2-1
=7(x1+x2)-2
=7*1-2
=5