Biªn so¹n : GV NguyÔn Trung §¨ng Vµi bµi to¸n ph¬ng tr×nh
1 Gi¶i vµ biÖn luËn c¸c ph¬ng tr×nh sau
1)(m−1)x2−2(m−1)x m+ + =1 0 2)(x−2m+1) (mx−3m x+ =) 0 3)x+ =1 mx−2
4) (m - 2)x2 - 2(m + 1)x + m = 0 5) (m2 - 4)x2 + 2(m + 2)x + 1 = 0 6)(m3 - 4m)x2 + 2(m - 2)x + 1 = 0
−a
x
a
4
a x 2
x 3
7 m x
x m
x
m
= +
−
2
a x
a 8 a x
a 2 a x
x
−
= +
−
2 2
2 2
a x
b a a x
b a x
a
x
b
a
x
−
+
−
−
− +
=
+
+
+
−
+
1 x
1 b
1 a
1
+ +
= +
b a
b a b a
b a x
1 x
−
+ + +
−
=
15) x2 + mx + m = 0
16) (a2 + a + 1)x2 + (2a - 3)x + a - 5 = 0 17) x2 - 6ax + 2 - 2a + 9a2 = 0 18) x2 - 2x + 1 - a2 = 0
19) (m - 1)x2 - (2m - 1)x + m + 5 = 0 20) (2 - a)x2 - 3ax + 2a = 0 21) (k + 1)x2 - kx + 1 = 0
22) ax2 + x + 1 = 0 23) (m2 - 1)x2 + 2(m - 1)x + 1 = 0 24) m(m + 2)x2 + 2(m - 1)x + 1 = 0 25) (a2 - 5a + 4)x2 + (a -4)x + 4 = 0. 26) (m2 - 4)x2 + (m + 2)x + 1 = 0 27) (m2 - 3m + 2)x2 +2(m - 1)x +1 = 0 28) (m2 - 5m + 6)x2 + (m - 3)x + 1 = 0 29) 2 3
0 2
x a
x a− − =
− + 30) (a - 1)x2 - 2x - a = 0 31) mx2 - 4x - 3m + 1 = 0.
32)x a x a a + a =0
− + 33)
x+ a x= a
+ 34) (a - 1)x2 - 2x - a = 0 35)x2 + mx + 1 = 0 36)(x - 3a)(x - a - 3) = 0
37) x2 - (m + 1)x + 3m - 5 = 0 38) (2m + 1)x2 - 4x - 2m + 1 = 0 39) mx2 + (3 - m)x + 1 = 0 40)x2 - 6ax + 2 - 2a + 9a2 = 0 41) 2(m - 1)x2 - 4x + m = 0
2 Gi¶i c¸c PT sau
1 10x+6=9−x 2 x2 − x+7= x−3 3 x+9+ x−5=8 5 x2 −12x+5= x−5
6
2
3 x 1 x 2 x 1
x
2
2 4 x x 4 x
x− − + + − = 8 x2+ x+9=x−15
9 1+x− 4−x =1 11 x2 − x+2= x−5 12 x−x2 =4−x 13 x 1
1 x
1
x2
−
=
−
−
14 x+4− x+1= x+3 15 x2 + 9 = 6x + 4 x2− x+6 16 x2 + 3 - (x 4)
2
3 2 x
x2 − + = +
17 x2 −12x+7+ x−x2 =0 18 (x - 3)2 + 3x - 22 = x2 − x+7 19 (x - 3)(x + 1) +4(x - 3)
3 x
1 x
− + = -3
20 x2 + 2 x2− x+1= x+4 21 -x2 + 2x + 4 (x−3)(x+1)=10 22 3+x+ 6−x+ (3+x)(6−x)=3
26 33 x2− x+2= x2− x+5 27 4 x− x2−1+ x+ x2 −1=2 28 x + 17−x2 +x. 17−x2 =−2
3 2
3 (x+1)2 +4 (x−1) =6 (x −1)
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Trang 2Biªn so¹n : GV NguyÔn Trung §¨ng
x
) 1 x ( 2 1
x
+ 33 x2 +10x+1=7− x−x2 34 2(x - 1) x2+ x−1=x2 − x−1
x
1 x x 2
5
2 x
1 x 4 1 x
2 x
=
−
+ +
+
6 1 x 8 15 x 1 x 4 3
x+ + − + + − − =
41 4 x + 2 = x + 1 + 4 42 x+ 1−x+2 x(1−x)−24 x(1−x)=1 43 x4 − x2 +1=1−x
44 x + 3 − 4 x − 1 + x + 8 − 6 ( x − 1 = 1 45 x
x x
x 2
3 x x x x
+
=
−
−
3 x
x
=
−
−
−
47 x2 + x+5=5 48 x2 + x2+1=1 49 3 x − 1 +3 x − 2 =3 x − 3 50 4 x +417 − x = 3
51 3 x − 2 + x + 1 = 3 52 3 24 + x + 12 − x = 6 53 2 x − 1 −3 x − 3 =3 2 54 x 1
2
1 x 2
1
55 3 x + 1 −3 x − 1 =6 x2 − 1 56 x+3+ 6−x − (3+x)(6−x)=3 57 3 x + 34 −3 x − 3 = 1
58 x3 + 1 = 23 2 x − 1 59 312 − x +314 + x = 2 60 3 x − 1 = x316 −3 x + 1
61 x+ 1−x2 =x 1−x2 62 x3 + (1−x2)3 =x 2− x2 63 1−2 x4 −x2 =x−1
64 3+ 9−x2 − 3− 9−x2 = 3−x 65 x+ x + x− x =2 66.
14 49 x 14 x 49
x
14
67 x−2+ x−5+ x+2+3 x−5=7 2 68 x+ x−9 = 6− x− x−9
69 x+2 x−1+ x−2 x−1=x−1 70 3 3
x 1
x 3 x 3
x 1
−
+ + +
− =2 71
4 1 x
1 x 1 x
1
+
− +
− +
x 16
1 x 1
x
x
16
5
1 x 2
1 x
73 x2− x+2+ x2 − x+3=2 x2 − x+4 74 x2 −x−2+ x2 − x−3=2 x2 − x−4
75 1+ x 1−x2 + x2 =1 76 4 (x−1)2 −4 (x+1)2 =234 x2 −1
77 x+ x+7+ x2+ x=35− x 78 x + 2 ( 1 + x + 1 ) + x + 2 ( 1 − x + 1 ) = x
79 x2−x −2=0 80 7x(x−2)=x+18 81 x−2 = x2− x+3
82 x2− x−2=0 83 x 2 − x + 2 = 1 − 2 x 84 x 2 − x = x 2 − 1
2 http://toanphothong.violet.vn