Solving A Nice Cubic Equation

[@mirandak3273]

After you substituted y - (1/3) for x, in the third line you got (y^3) - (1/3)y = 3/216 because ‘if you subtract 1 over 9 from 1 over 8 that’s what you get” ie 3/216. But you forgot about the 1/27 you have to add. It really should be (y^3) - (1/3)y = 11/216. It’s good you quit working that solution as the results would have been incorrect due to that error.

[@roodvleven3239]

Nice problem. Thanks. Suggestion: workout the answer before you record the video. The little mistakes make it more difficult to follow. Keep it up👍

[@ShortsOfSyber]

Thanks

[@wes9627]

-1/8+1/4=1/8

[@barakathaider6333]

👍

[@prollysine]

8x^3+8x^2+/-x-1=0 , (2x+1)(4x^2+2x-1)=0 , 2x= -1 , x=-1/2 , 4x^2+2x-1=0 , x=(-2+/-V(4+16))/8 , x= (-1+V5)/4 , (-1-V5)/4 , 8 4 solu , x= -1/2 , (-1+V5)/4 , (-1-V5)/4 , 4 2 -2 -1

[@walterwen2975]

Solving A Nice Cubic Equation: x³ + x² = 1/8; x =? 8(x³ + x²) = 1, 8x³ + 8x² - 1 = 0, (8x³ + 1) + (8x² - 2) = 0 [(2x)³ + 1] + 2[(2x)² - 1] = (2x + 1)[(4x² - 2x + 1) + 2(2x - 1)] = 0 (2x + 1)(4x² + 2x - 1) = 0, 2x + 1 = 0 or 4x² + 2x - 1 = 0 2x = - 1, x = - 1/2 or x = (- 2 ± 2√5)/8 = (- 1 ± √5)/4 Answer check: x = - 1/2: x³ + x² = (- 1/2)³ + (- 1/2)² = 1/4 - 1/8 = 1/8; Confirmed x = (- 1 ± √5)/4: 4x² + 2x - 1 = 0, x² = (1 - 2x)/4 = 1/4 - x/2 x³ = x(x²) = x(1/4 - x/2) = x/4 - x²/2 = x/4 - (1/2)(1/4 - x/2) = x/2 - 1/8, x³ + x² = (x/2 - 1/8) + (1/4 - x/2) = 1/4 - 1/8 = (2 - 1)/8 = 1/8; Confirmed Final answer: x = - 1/2; x = (- 1 + √5)/4 or x = (- 1 - √5)/4

[@bobbyheffley4955]

The solutions are the cosines of 120°, 72°, and 144°.