让x是一个实数,即x^3+4x=8. 确定x^7+64x^2的值.
给出方程 x^3 + 4x = 8,我们可以解决 x^3: x^3 = -4x + 8 现在我们可以通过替换 x^3 来找到 x^3 的高位数: - x^4 = 4x^2 - 8x - x^5 = -4x^3 + 8x^2 = -4x^4x + 8) + 8x^2 = 8x^2 + 16x - 32 - x^6 = 8x^3 + 16x^2 - 32x = 8x^4x + 8) + 16x^2 - 32x = 16x^2 - 64x + 64x + 64x + 16x^7 = 16x^3 - 64x^2 + 64x = 16x^4x + 8) - 64x^2 + 64x = 128 - 64x^2 因此,我们可以表达 x^7 + 64x^2 = x^7 + 64x^2 = 128x^2 + 64x^2 + 64x^2 = 12x^8 x^2 = 12x^2 x^2