3(x^2-1)^2+18(1-x^2)+273(x²-1)²+18(1-x²)+27

问题描述:

3(x^2-1)^2+18(1-x^2)+27
3(x²-1)²+18(1-x²)+27

=3【(x²-1)²-6(x²-1)+9】
=3(x²-1-3)²
=3(x²-4)²
= 3(x-2)²(x+2)²

1)3(x²-1)²+18(1-x²)+27=0
2)(1-x²)²+6(1-x²)+9=0
3) (1-x² + 3)² = 0
4) 1-x² + 3 = 0
5) x² = 4
6) x = 2, x = -2

原式=3(x²-1)²-18(x²-1)+27
=3[(x²-1)²-6(x²-1)+9]
=3(x²-1-3)²
=3(x²-4)²
=3(x+2)²(x-2)²