Let x be a real number such that x3+4x=8. Determine the value of x7+64x2.
Solution — click to reveal
From the equation x3+4x=8,x3=−4x+8. Then x4x5x6x7=−4x2+8x,=−4x3+8x2=−4(−4x+8)+8x2=8x2+16x−32,=8x3+16x2−32x=8(−4x+8)+16x2−32x=16x2−64x+64,=16x3−64x2+64x=16(−4x+8)−64x2+64x=128−64x2.Hence, x7+64x2=128−64x2+64x2=128.