Question

一道一元二次方程题

如图

Answer 1

（1）(3x+1)^2=7 解：(3x+1)^2=7 ∴(3x+1)^2=7 ∴3x+1=±√7(注意不要丢解) ∴x= (±√7-1)/3 （2）9x^2-24x+16=11 解： 9x^2-24x+16=11 ∴(3x-4)^2=11 ∴3x-4=±√11 ∴x= (±√11+4)/3 ∴原方程的解为x1=(√11+4)/3 x2=(-√11+4)/3 (3) (x+3)(x-6)=-8 解：(x+3)(x-6)=-8 化简整理得 x^2-3x-10=0 (方程左边为二次三项式，右边为零) (x-5)(x+2)=0 (方程左边分解因式) ∴x-5=0或x+2=0 (转化成两个一元一次方程) ∴x1=5,x2=-2是原方程的解。 (4) 2x^2+3x=0 解：2x^2+3x=0 x(2x+3)=0 (用提公因式法将方程左边分解因式) ∴x=0或2x+3=0 (转化成两个一元一次方程) ∴x1=0，x2=-3/2是原方程的解。 注意：有些同学做这种题目时容易丢掉x=0这个解，应记住一元二次方程有两个解。 (5) 6x^2+5x-50=0 (选学）解：6x2+5x-50=0 (2x-5)(3x+10)=0 (十字相乘分解因式时要特别注意枝凯符号不要出错) ∴2x-5=0或3x+10=0 ∴x1=5/2, x2=-10/3 是原方程的解。 (6)x^2-4x+4=0 （选学）解：x^2-4x+4 =0 （∵4 可分解为2 ·2 ，∴此题可用因式分解法） (x-2)(x-2 )=0 ∴x1=2 ,x2=2是原方程的解。 (7)（x-2）^2=4（2x+3）^2 解.(x-2)^2-4(2x+3)^2=0. [x-2+2(2x+3)][(x-2-2(2x+3)=0. (5x+4)(-5x-8)=0. x1=-4/5, x2=-8/5 （8）y^2+2√2y-4=0 解(y+√2)^2-2-4=0. (y+ √2)^2=6. y+√2=√6. y=-√2±√6. y1=-√2+√6； y2=-√2-√6. （9）（x+1）^2-3（x+1)+2=0 解(x+1-1)(x+1-2)=0. x(x-1)=0. x1=0, x2=1. （10）x^2+2ax-3a^2=0（a为信搭宏常数）解 (x+3a)(x-a)=0. x1=-3a, x2=a. (11)2x^2＋7x＝4．滑册解：方程可变形为2x^2＋7x－4＝0． ∵a＝2，b＝7，c＝－4，b2－4ac＝72－4×2×(－4)＝81＞0， ∴x＝ ．∴x1＝ ，x2＝－4． (12)x^2－1＝2 x 解：方程可变形为x^2－2 x－1＝0． ∵a＝1，b＝－2 ，c＝－1，b2－4ac＝(－2 )2－4×1×(－1)＝16＞0． ∴x＝ ．∴x1＝ ＋2，x2＝ －2 （13） x^2 + 6x+5=0 解：原方程可化为(x+5)(x+1)=0 x1=-5 x2=-1 (14) x ^2－4x+ 3=0 解：原方程可化为(x-3)(x-1)=0 x1=3 x2=1 (15)7x^2 －4x－3 =0 解原方程可化为 (7x+3)(x-1)=0 x1=-3/7 x2=1 (16)x ^2－6x+9 =0 解原方程可化为 (x-3)^2=0 x1=x2=3 (17)x2+8x+16=9 解：(x+4)2=9 x+4=3或x+4=-3 x1=-1,x2=-7 (18)(x2-5)2=16 解：x2-5=4或x2-5=-4 x2=9或x2=1 x1=3,x2=-3,x3=1,x4=-1 (19)x(x+2)=x(3-x)+1 解x2+2x=3x-x2+1 2x2-x-1=0 (2x+1)(x-1)=0 x1=-1/2 x=1 (20) 6x^2+x-2=0 解原方程可化为(3x+2)(2x-1)=0 (x+2/3)(x-1/2)=0 x1=-2/3 x2=1/2 这是20道有过程的，还有一些没有过程，只有答案的。 1)x^2-9x+8=0 答案：x1=8 x2=1 (2)x^2+6x-27=0 答案：x1=3 x2=-9 (3)x^2-2x-80=0 答案：x1=-8 x2=10 (4)x^2+10x-200=0 答案：x1=-20 x2=10 (5)x^2-20x+96=0 答案：x1=12 x2=8 (6)x^2+23x+76=0 答案：x1=-19 x2=-4 (7)x^2-25x+154=0 答案：x1=14 x2=11 (8)x^2-12x-108=0 答案：x1=-6 x2=18 (9)x^2+4x-252=0 答案：x1=14 x2=-18 (10)x^2-11x-102=0 答案：x1=17 x2=-6 (11)x^2+15x-54=0 答案：x1=-18 x2=3 (12)x^2+11x+18=0 答案：x1=-2 x2=-9 (13)x^2-9x+20=0 答案：x1=4 x2=5 (14)x^2+19x+90=0 答案：x1=-10 x2=-9 (15)x^2-25x+156=0 答案：x1=13 x2=12 (16)x^2-22x+57=0 答案：x1=3 x2=19 (17)x^2-5x-176=0 答案：x1=16 x2=-11 (18)x^2-26x+133=0 答案：x1=7 x2=19 (19)x^2+10x-11=0 答案：x1=-11 x2=1 (20)x^2-3x-304=0 答案：x1=-16 x2=19 (21)x^2+13x-140=0 答案：x1=7 x2=-20 (22)x^2+13x-48=0 答案：x1=3 x2=-16 (23)x^2+5x-176=0 答案：x1=-16 x2=11 (24)x^2+28x+171=0 答案：x1=-9 x2=-19 (25)x^2+14x+45=0 答案：x1=-9 x2=-5 (26)x^2-9x-136=0 答案：x1=-8 x2=17 (27)x^2-15x-76=0 答案：x1=19 x2=-4 (28)x^2+23x+126=0 答案：x1=-9 x2=-14 (29)x^2+9x-70=0 答案：x1=-14 x2=5 (30)x^2-1x-56=0 答案：x1=8 x2=-7 (31)x^2+7x-60=0 答案：x1=5 x2=-12 (32)x^2+10x-39=0 答案：x1=-13 x2=3 (33)x^2+19x+34=0 答案：x1=-17 x2=-2 (34)x^2-6x-160=0 答案：x1=16 x2=-10 (35)x^2-6x-55=0 答案：x1=11 x2=-5 (36)x^2-7x-144=0 答案：x1=-9 x2=16 (37)x^2+20x+51=0 答案：x1=-3 x2=-17 (38)x^2-9x+14=0 答案：x1=2 x2=7 (39)x^2-29x+208=0 答案：x1=16 x2=13 (40)x^2+19x-20=0 答案：x1=-20 x2=1 (41)x^2-13x-48=0 答案：x1=16 x2=-3 (42)x^2+10x+24=0 答案：x1=-6 x2=-4 (43)x^2+28x+180=0 答案：x1=-10 x2=-18 (44)x^2-8x-209=0 答案：x1=-11 x2=19 (45)x^2+23x+90=0 答案：x1=-18 x2=-5 (46)x^2+7x+6=0 答案：x1=-6 x2=-1 (47)x^2+16x+28=0 答案：x1=-14 x2=-2 (48)x^2+5x-50=0 答案：x1=-10 x2=5 (49)x^2+13x-14=0 答案：x1=1 x2=-14 (50)x^2-23x+102=0 答案：x1=17 x2=6 (51)x^2+5x-176=0 答案：x1=-16 x2=11 (52)x^2-8x-20=0 答案：x1=-2 x2=10 (53)x^2-16x+39=0 答案：x1=3 x2=13 (54)x^2+32x+240=0 答案：x1=-20 x2=-12 (55)x^2+34x+288=0 答案：x1=-18 x2=-16 (56)x^2+22x+105=0 答案：x1=-7 x2=-15 (57)x^2+19x-20=0 答案：x1=-20 x2=1 (58)x^2-7x+6=0 答案：x1=6 x2=1 (59)x^2+4x-221=0 答案：x1=13 x2=-17 (60)x^2+6x-91=0 答案：x1=-13 x2=7 (61)x^2+8x+12=0 答案：x1=-2 x2=-6 (62)x^2+7x-120=0 答案：x1=-15 x2=8 (63)x^2-18x+17=0 答案：x1=17 x2=1 (64)x^2+7x-170=0 答案：x1=-17 x2=10 (65)x^2+6x+8=0 答案：x1=-4 x2=-2 (66)x^2+13x+12=0 答案：x1=-1 x2=-12 (67)x^2+24x+119=0 答案：x1=-7 x2=-17 (68)x^2+11x-42=0 答案：x1=3 x2=-14 (69)x^20x-289=0 答案：x1=17 x2=-17 (70)x^2+13x+30=0 答案：x1=-3 x2=-10 (71)x^2-24x+140=0 答案：x1=14 x2=10 (72)x^2+4x-60=0 答案：x1=-10 x2=6 (73)x^2+27x+170=0 答案：x1=-10 x2=-17 (74)x^2+27x+152=0 答案：x1=-19 x2=-8 (75)x^2-2x-99=0 答案：x1=11 x2=-9 (76)x^2+12x+11=0 答案：x1=-11 x2=-1 (77)x^2+17x+70=0 答案：x1=-10 x2=-7 (78)x^2+20x+19=0 答案：x1=-19 x2=-1 (79)x^2-2x-168=0 答案：x1=-12 x2=14 (80)x^2-13x+30=0 答案：x1=3 x2=10 (81)x^2-10x-119=0 答案：x1=17 x2=-7 (82)x^2+16x-17=0 答案：x1=1 x2=-17 (83)x^2-1x-20=0 答案：x1=5 x2=-4 (84)x^2-2x-288=0 答案：x1=18 x2=-16 (85)x^2-20x+64=0 答案：x1=16 x2=4 (86)x^2+22x+105=0 答案：x1=-7 x2=-15 (87)x^2+13x+12=0 答案：x1=-1 x2=-12 (88)x^2-4x-285=0 答案：x1=19 x2=-15 (89)x^2+26x+133=0 答案：x1=-19 x2=-7 (90)x^2-17x+16=0 答案：x1=1 x2=16 (91)x^2+3x-4=0 答案：x1=1 x2=-4 (92)x^2-14x+48=0 答案：x1=6 x2=8 (93)x^2-12x-133=0 答案：x1=19 x2=-7 (94)x^2+5x+4=0 答案：x1=-1 x2=-4 (95)x^2+6x-91=0 答案：x1=7 x2=-13 (96)x^2+3x-4=0 答案：x1=-4 x2=1 (97)x^2-13x+12=0 答案：x1=12 x2=1 (98)x^2+7x-44=0 答案：x1=-11 x2=4 (99)x^2-6x-7=0 答案：x1=-1 x2=7 (100)x^2-9x-90=0 答案：x1=15 x2=-6 (101)x^2+17x+72=0 答案：x1=-8 x2=-9 (102)x^2+13x-14=0 答案：x1=-14 x2=1 (103)x^2+9x-36=0 答案：x1=-12 x2=3 (104)x^2-9x-90=0 答案：x1=-6 x2=15 (105)x^2+14x+13=0 答案：x1=-1 x2=-13 (106)x^2-16x+63=0 答案：x1=7 x2=9 (107)x^2-15x+44=0 答案：x1=4 x2=11 (108)x^2+2x-168=0 答案：x1=-14 x2=12 (109)x^2-6x-216=0 答案：x1=-12 x2=18 (110)x^2-6x-55=0 答案：x1=11 x2=-5 (111)x^2+18x+32=0 答案：x1=-2 x2=-16