解
2x2−6x+6=c1(x2+x−1)+c2(x2−x+1)
解
x=2(2−c2−c1)6−c2+c1+5c12+28c1−2c1c2+20c2−3c22−12,x=2(2−c2−c1)6−c2+c1−5c12+28c1−2c1c2+20c2−3c22−12;2−c2−c1=0
解答ステップ
2x2−6x+6=c1(x2+x−1)+c2(x2−x+1)
拡張 c1(x2+x−1)+c2(x2−x+1):c1x2+c1x−c1+c2x2−c2x+c2
2x2−6x+6=c1x2+c1x−c1+c2x2−c2x+c2
両辺から−c2x+c2を引く2x2−6x+6−(−c2x+c2)=c1x2+c1x−c1+c2x2−c2x+c2−(−c2x+c2)
簡素化
2x2−6x+6+c2x−c2=c1x2+c1x−c1+c2x2
c2x2を左側に移動します
2x2−6x+6+c2x−c2−c2x2=c1x2+c1x−c1
両辺からc1x−c1を引く2x2−6x+6+c2x−c2−c2x2−(c1x−c1)=c1x2+c1x−c1−(c1x−c1)
簡素化
2x2−6x+6+c2x−c2−c2x2−c1x+c1=c1x2
c1x2を左側に移動します
2x2−6x+6+c2x−c2−c2x2−c1x+c1−c1x2=0
標準的な形式で書く ax2+bx+c=0(2−c2−c1)x2+(−6+c2−c1)x+6−c2+c1=0
解くとthe二次式
x1,2=2(2−c2−c1)−(−6+c2−c1)±(−6+c2−c1)2−4(2−c2−c1)(6−c2+c1)
簡素化 (−6+c2−c1)2−4(2−c2−c1)(6−c2+c1):5c12+28c1−2c1c2+20c2−3c22−12
x1,2=2(2−c2−c1)−(−6+c2−c1)±5c12+28c1−2c1c2+20c2−3c22−12;2−c2−c1=0
解を分離するx1=2(2−c2−c1)−(−6+c2−c1)+5c12+28c1−2c1c2+20c2−3c22−12,x2=2(2−c2−c1)−(−6+c2−c1)−5c12+28c1−2c1c2+20c2−3c22−12
x=2(2−c2−c1)−(−6+c2−c1)+5c12+28c1−2c1c2+20c2−3c22−12:2(2−c2−c1)6−c2+c1+5c12+28c1−2c1c2+20c2−3c22−12
x=2(2−c2−c1)−(−6+c2−c1)−5c12+28c1−2c1c2+20c2−3c22−12:2(2−c2−c1)6−c2+c1−5c12+28c1−2c1c2+20c2−3c22−12
二次equationの解:x=2(2−c2−c1)6−c2+c1+5c12+28c1−2c1c2+20c2−3c22−12,x=2(2−c2−c1)6−c2+c1−5c12+28c1−2c1c2+20c2−3c22−12;2−c2−c1=0