已知2x^2-3=0,求代数式x^2(x^2-1)^2+x^2(5-x^2)^2-9的值

问题描述:

已知2x^2-3=0,求代数式x^2(x^2-1)^2+x^2(5-x^2)^2-9的值

2x^2-3=0
x^2=3/2
x^2(x^2-1)^2+x^2(5-x^2)^2-9=3/2(3/2-1)^2+3/2(5-3/2)^2-9=3/8+147/8-9=78/8=39/4

39/4

解方程得x=3/4,代入到后面式子中求出值为3.

“^”这是啥?乘号还是。。

2x^2-3=0→x^2=3/2
代数式x^2(x^2-1)^2+x^2(5-x^2)^2-9
=3/2(3/2-1)^2+3/2(5-3/2)^2-9
=3/2(1/2)^2+3/2(7/2)^2-9
=3/2(1/4+49/4)-9
=3/2×25/2-9
=75/4-9
=39/4

2x²-3=0
2x²=3
x²=3/2
x²(x²-1)²+x²(5-x²)²-9
=x²[x^4-2x²+1+25-10x²+x^4]-9
=2x²(x^4-6x²+13)-9
=2x²[(x²-3)²+4]-9
=3(9/4+4)-9
=75/4-36/4
=39/4

9.75