Chuong III Ds

8/8/2019 Chuong III Ds

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PHNG TRNH BC NHT V BC HAI MT N

Bi 1:. Gii v bin lun cc phng trnh sau :

a) (m2 + 2)x 2m = x 3 b) m(x m + 3) = m(x 2) + 6

c) m2(x 1) + m = x(3m 2) d) m2x = m(x + 1) 1

e) m2

(x 3) +10m = 9x + 3 f) m3

x m2

4 = 4m(x 1)

g) (m +1)2x + 1 m = (7m 5)x h) a

2x = a(x + b) b

i) (a + b)2x + 2a

2= 2a(a + b) + (a

2+ b

2)x

Bi 2:a) nh m phng trnh (m2 3)x = 2mx + m 1 c tp nghim l Rb) nh m phng trnh (mx + 2)(x + 1) = (mx + m2)x c nghim duy nhtc) nh a ; b phng trnh (1 x)a + (2x + 1) b= x + 2 v s nghim xR

d) nh m phng trnh m2x = 9x + m2 4m + 3 v s nghim xR

Bi 3: Gii v bin lun phng trnh theo tham s m:a) mx2 + 2x + 1 = 0b) 2x

2 6x + 3m 5 = 0

c) (m2 5m 36)x2 2(m + 4)x + 1 = 0

Bi 4: Cho a ; b ; c l 3 cnh ca . Chng minh rng phng trnh sau v nghim

a2x2 + (c2 a2 b2)x + b2 = 0

Bi 5: Cho a ; b ; c 0 v 3 phng trnh ax2 + 2bx + c = 0 ; bx2 + 2cx + a = 0; cx2 + 2ax + b = 0.

Chng minh rng t nht 1 trong 3 phng trnh c nghim

Bi 6: Cho phng trnh : x2 + 2x = a. Bng th , tm cc gi tr ca a phng trnh cho c nghim ln

hn 1. Khi , hy tm nghim ln hn 1 Bi 7: Gi s x1 ; x2 l cc nghim ca phng trnh : 2x2 11x + 13 = 0. Hy tnh :

a) x13

+ x23

b) x14

+ x24

c) x14

- x24

d)

2

1

2

x

x

+

2

2

1

x

x

Bi 8:Cc h s a, b , c ca phng trnh trng phng : ax4 + bx2 + c = 0 phi tha iu king phng trnh :a) V nghim b) C mt nghim c) C hai nghim d)C ba nghim e)C bn nghimBi 9: Gii v bin lun:

a) (m 2)x2

2(m 1)x + m 3 = 0 b) (m 1)x2

2mx + m + 1 = 0

Bi 10: Cho phng trnh : x2 2(m 1)x + m2 3m = 0

a) nh m phng trnh c nghim x1 = 0. Tnh nghim x2.

b) nh m phng trnh c 2 nghim phn bit x1 ; x2 tha x12 + x2

2 = 8

Bi 11: Cho phng trnh : mx2 2(m 3)x + m 6 = 0

a) CMR: phng trnh lun c nghim x1 = 1 ; m. Tnh nghim x2.

b) nh m phng trnh c 2 nghim phn bit tha1 2

1 11

x x


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a) nh m phng trnh c 2 nghim tri du c gi tr tuyt i bng nhauBi 12: Gi s phng trnh ax2 + bx + c = 0 c 2 nghim dng phn bit x1 ; x2.

a) CMR phng trnh cx2 +bx + a = 0 cng c 2 nghim dng phn bit x3 ; x4.

b) CMR x1 + x2 + x3 + x4 4

Bi 13: Cho phng trnh (m +2)x2 2(4m 1)x 2m + 5= 0

a) nh m phng trnh c nghim kp. Tnh nghim kp b) Tm h thc c lp i vi m gia cc nghim . suy ra nghim cu a

Bi 14: Cho 2 s x1; x2 tha h

(x1+ x2) 2 x1 x2 = 0

m x1x2 (x1+ x2) = 2m + 1 (Vi m 2)

a) Lp phng trnh c 2 nghim x1; x2

b) nh m phng trnh c nghim

c) nh m phng trnh c 2 nghim phn bit l 2 cnh tam gic vung c cnh huyn = 2

Bi 15: Cho 2 phng trnh x2 + b1x + c1 = 0 v x2

+ b2x + c2 = 0 tha b1b2 2(c1 + c2 )

Chng minh rng t nht 1 trong 2 phng trnh c nghim

Bi 16: Cho phng trnh x2 2(m 1)x + m2 3m + 4 = 0

a) nh m phng trnh c 2 nghim tha x12

+ x22

= 20

b) nh m phng trnh c nghim kp. Tnh nghim kp

c) Tm h thc c lp gia 2 nghim. Suy ra gi tr nghim kp

MT S PHNG TRNH QUY V PHNG TRNH BC NHT HOC BC HAI

Bi 1: Gii v bin lun cc phng trnh

a) mx x + 1 = x + 2 b) mx + 2x 1 = x

c) mx 1 = 5 d) 3x + m = 2x 2m

Bi 2: Tm cc gi tr tham s m sao cho phng trnh mx 2=x + 4c nghim duy nht.

Bi 3: Gii v bin lun cc phng trnh (m, a v k l nhng tham s)

a) 12ax

1

2x

a

b) 11x

3mmx

c)3x

kx

3x

k3x

d)1

x m

x

+

x 2

x

= 2

e)2

x

mx+

mx

x

2= 2 f )

1 x

x m

+

mx

x

2=

2 2

2(x m) 2

m x


3/6

Bi 4:Gii cc phng trnh

a) x31xx2 b) 12x96xx2

Bi 5: Gii v bin lun cc phng trnh

a) 01x1)(mx b) 2a2x

12a

Bi 6:Gii cc phng trnh (bng cch t n ph)

a) 4x2

12x 5 01112x4x2

b) x2

+ 4x 3 x + 2 + 4 = 0

c) 4x2

+ 06x

12x

x

12

d) x2

x +2x x 9 = 3

e) x2 + 22x 3x 11 = 3x + 4

f) x2 + 3 x 10 + 3 x(x 3) = 0

Cu 7: nh tham s phng trnh

a)1

x

mx=

1

1

x

xc nghim duy nht

d)mx

x

2

+x

x 1= 2 v nghim

H PHNG TRNH BC NHT HAI N

Bi 1: Bng nh thc gii cc h phng trnh

a)

89y7x

34y5xb)

0y3x22

1y2x3

Bi 2: Gii v bin lun h phng trnh sau:

a)

32m3mymx

1myxb)

m1)y(m2x

4mymx

c)

12)y(3a1)x(a

24)y(a2)x(ad)

mx y m 1

x my 2

Bi 3: Tm m, a, b sao cho h phng trnh sau c v s nghim


4/6

a)

m-1myx

2mymxb)

m32y6)x(m

m1my4x

c)

baybx

abyaxd)

ba)y(1bx

aby1)x(a

Bi 4: Tm m, a, b sau cho h phng trnh sau v nghim

a)

4by6x

2yaxb)

32m3mymx

1myxc)

m 12m

x y

1 mm 1

x y

Bi 5: Cho h phng trnh :4 2mx y m

x my m

a) Gii v bin lunb) nh m Z h c nghim duy nht l nghim nguyn

Bi 6: Cho h(m+1) x - 2y = m - 1

2 2m x - y = m + 2m

a) Gii v bin lun h phng trnhb) Tm tt c cc gi tr nguyn ca m h c nghim duy nht l nghim nguyn

Bi 7 : nh m nguyn h c nghim duy nht l nguyn :

2mmyxm

1m2y1)x(m22

Bi 8:: Cho h2x y 3m 3

x +2y = 4 -m

a) Gii h phng trnh

b) Tm tt c cc gi tr ca m x2 + y2t gi tr nh nht

Bi 9 : Cho h2y x 10m 5

x + y = 52

. Vi gi tr no ca m th tch 2 nghim x.y t gi tr ln nht

a) m = 2 b) m = 8 c) m = -1

8d) Kt qu khc


5/6

Bi 10: Gii

a)

28

3 3 100

4 5z 107

x y z

5x y z

2x y

b)

2 2

5 5

4z 8

x-3y z

-2x y z

3x-7y

c)

2

2 8

z 5

-x+5y z

2x-9y z

3x-4y

H PHNG TRNH BC HAI 2 N

Bi 1: Gii cc h phng trnh

a)

164yx

2yx22

b)

1y2x

7y5xyx22

c)

042y2xxy

07y2x22

d)

03yx6xy3x

69y4x2


a)22

11

30

x y xy

y xyx

b)

30

35

x y y x

x x y y

c)

22

4

28

xy

yx

d)

22

2

4

x y xy

xyyx

e)22

7

2

5

2

x y xy

y xyx

f)22

3

1

x y xy

xyyx

g)

22

3

6

xy x y

x y xyyx

h)

22

2

164

x y

yx

i)22

1 1 2

4

( ) ( ) x x y y y

x yyx

j)

33

1

61

x y

yx

k)

33

2

2

( ) xy x y

yx

l)

513

6

x y

x y

y x

m)22

6

2 2( )

x y

xyyx

n)

22

5

6

x y xy

y xyx

o)

22

1 1 18

65

( )( )x y

yx

p)

22

22

1333

3 1

xy yx

xy yx

q)

3

722

22

xyyx

xyyxr)

0

1222

2

xyyx

xyyx )(s)

5yxyx

7yxyx22

t)

160

322

yx

xyyx )(


a)

2

2

2x +xy= 3x

2y + xy= 3y

b)2

2

x -2x=y

y -2y=x

c)

2 2

2 2

x -2y = 2x + y

y -2x =2y + x

d)

2

2

x = 3x+2y

y =3y+2y

Bi 4: Gii v bin lun h phng trnh :

mxy

4yx


6/6

Bi 5: Cho h phng trnh22

4x y

myx

a) Gii h khi m =10 b) Gii v bin lun hphng trnh trn theo m

Bi 6: Cho hx y xy m 1

(x y)xy m

a) Gii h khi m =2 b) nh m h c nghim

Bi 7: Cho h phng trnh22 2

1

2

x y m

xyyx m

a) Gii h khi m = 5 b) nh m h c nghimBi 8: Cho h phng trnh

22

x y xy m

myx

a) Gii h khi m =5 b) Gii v bin lun h phng trnh trn theo m

Bi 9: Cho h phng trnh2

22

4

2 1

( )

( )

x y

myx

a) Gii h khi m =10 b) Gii v bin lun h phng trnh trn theo m

Bi 10 : nh m h phng trnh sau c nghim duy nht :

mx4xxy

my4yyx232

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Chuong III Ds