求一个因式分解的过程 6x-5/9=-5/9(x-3/5)²+5

5个回答

  • 6x-5/9=-5/9(x-3/5)²+5

    6x-5/9=-5x²/9+2x/3-1/5+5=-5x²/9+2x/3+24/5

    5x²/9-2x/3-24/5+6x-5/9=5x²/9+16x/3-241/45=0

    25x²+240x-241=0

    x²+48x/5-241/25

    =﹙x+24/5﹚²-﹙24/5﹚²-241/25

    =﹙x+24/5﹚²-817/25

    =[x+﹙24+√817﹚/5]×[x+﹙24-√817﹚/5]=0

    ∴x=-﹙24+√817﹚/5]或x=-﹙24-√817﹚/5]