, , 02.07.2013.: , j , , j

J

1. j j (m 1)x2 2(3m 1)x m = 0, j m m 6= 1. m j j .

j j m j j D 0. j D = (2(3m1))24(m1)(m) = 4(9m26m+1+m2m) = 4(10m27m+1), j 10m2 7m+ 1 0 j m (, 15 ] [ 12 , 1) (1,+).

2. j 2x3|2x|7x4 = 1.

j j 7x 4 6= 0, tj. x R \ { 47}, j 2x3|2x|7x4 = 1 3|2 x| = 5x 4. j |2 x| =

{2 x , x 22 + x , x > 2 :

x 2 j j 3 (2 x) = 5x 4 2x = 2 x = 1. j x = 1 < 2 x = 1 j j.

x > 2 j j 3 (2 + x) = 5x 4 8x = 10 x = 54 . j x = 54 < 2 x = 54 j j.

3.

(a) j j 4x 3x2 = 5 3x1 + 4x1.4x 3x2 = 5 3x1 + 4x1 4x 4x1 = 5 3x1 + 3x2 4x 144x = 533x + 193x 344x = 169 3x 4x

3x =6427

(43

)x=(43

)3 x = 3. j j x = 3.

(b) j log21x1+x 1.

j j 1x1+x > 0 1 + x 6= 0, j. x (1, 1) .log2

1x1+x 1 1x1+x 2 1x1+x 2 0 13x1+x 0 x (1, 13 ].

P j j x (1, 13 ].

4. j j cos 2x sinx = 1.cos 2x sinx = 1 sinx = 2 sin2 x sinx (2 sinx+ 1) = 0 sinx = 0 2 sinx+ 1 = 0. sinx = 0 x = kpi, k Z, sinx = 12 x = pi6 + 2kpi, k Z x = 5pi6 + 2kpi, k Z. j j x {kpi|k Z} {pi6 + 2kpi|k Z} { 5pi6 + 2kpi|k Z}.

5. 200 l j j A, B C. j A 28% , j B C 4 : 5.

(a) j A, B C ? j A j j 200 : x = 100 : 28 = x = 56, j. 56 l jA. j 200 l 56 l = 144 l j B C. j B = 4y, C = 5y, j 4y + 5y = 144, j.y = 16, j 64 l j B, 80 l j C .

(b) , jj j B, j j B C 1 : 1? j B C 1 : 1, j 80 l j B, j. 80 l 64 l = 16 l j B. j j 200 : 16 = 100 : z, jz = 8%.