Aktivitas Mandiri 3.docx

AktivitasMandiri 3 1. Tentukanhimpunanpenyelesaiandari 5 x 2

-2x

= 0,2

Penyelesaian: 5 x2

-2x

= 5-1

5 x2

-2x

= 5-1

x2 - 2x + 1 = 0 (x - 1)2 = 0 x=1 2. Tentukanhimpunanpenyelesaiandari272x-3 = 9 Penyelesaian: 33(2x – 3) = 36x – 9 =

√ 243 243 1

1 2

36x – 9 = 35 ( 2 ) 5

36x – 9 = 3 2 5

36x – 9 = 3 2 6x – 9 =

5 2

12x – 18 = 5 12x = 23 x=

23 12

√3

3. Tentukanhimpunanpenyelesaiandari 102x-3 = 100.000 Penyelesaian: 102x-3 = 105 102x-3 = 105 2x – 3 – 5 = 0 2x – 8 = 0 2x = 8 x=4

4. Tentukanhimpunanpenyelesaiandari 3x : 27x + 2 = 729 x 93x Penyelesaian: 3x : 33(x + 2) = 36 x 32(3x) 3x : 33x + 6 = 36 x 36x 3-2x + 6 = 36 + 6x 3-2x + 6 = 36 + 6x -2x + 6 = 6 + 6x -2x + 6 – 6 – 6x = 0 -8x = 0 x = -8 5. Tentukanhimpunanpenyelesaiandari 25x = 4 x 8x + 7 Penyelesaian: 25x = 22 x 23(x + 7) 25x = 22 x 23x +21 25x = 2 3x + 23 25x = 23x + 23 5x – 3x – 23 = 0 2x – 23 = 0 2x = 23 23 x= 2

AktivitasMandiri 4 1. Tentukanhimpunanpenyelesaiandarisetiappersamaanberikutini. a. 103x – 12 = 1 b. 3 x 2 -6x+8 = 1 Penyelesaian: a. 103x – 12 = 100 103x – 12 = 100 3x – 12 = 0 3x = 12 x=4 b. 3 x 2 -6x+8 = 30 3 x 2 -6x+8 =30 x2– 6x + 8 = 0 (x – 4) (x – 2) = 0 x=4

x=2

HP { 4,2 } 2. Tentukanhimpunanpenyelesaiandaripersamaanberikutini. a. 7 x 2 +x-30 = 13 x 2 +x-30 b. 2 x 4 -16 = 5 x 4 -16 Penyelesaian: a. x2 + x – 30 = 0 (x + 6) (x – 5) = 0 x = -6 x = 5 HP {−6,5 } b. x4 – 16 = 0 (x2 – 4) (x2 + 4) = 0 x=2 x= -2 HP { 2,−2 } 3. Tentukanhimpunanpenyelesaiandaripersamaanberikutini. a. (2x + 5)2x+1 = 1

b. (x – 4)x + 2 = 1 Penyelesaian: a. 1) 2x + 1 = 0 −1 x= 2 2) 2x + 5 = 1 x = -2 3) 2x + 5 = -1 x = -3 −1 ,−2,−3 HP 2 b. 1) x + 2 = 0 x = -2 2) x – 4 = 1 x=5 3) x – 4 = -1 x=3 HP {−2,5, 3 } 4. Tentukanhimpunanpenyelesaiandaripersamaanberikutini. a. 32x – 10 x 3x + 9 = 0 b. 22x + 2 – 33 x 2x + 8 = 0

{

}

Penyelesaian: a. (3x)2 – 10 x 3x + 9 = 0 Misalkan 3x = b b2 – 10b + 9 =0 (b – 9) (b – 1) = 0 b=9 b=1 Substitusikan: 3x = 9 3x = 1 3x = 33 3x = 30 x 3 3 =3 3x = 30 x=3 x=0 HP { 3,0 }

b. 4. 2x – 33. 2x + 8 = 0 4(2x)2 – 33. 2x + 8 = 0 Misalkan 2x = q 4q2 – 33q + 8 = 0

32 )(q– 4 1 q=8 q= 4 Substitusikan: (q –

2x = 8

2x =

1 ) 4

1 4

2x = 23 2x = 2-2 x 3 2 =2 2x = 2-2 x=3 x = -2 HP { 3,−2 } 5. Tentukanhimpunanpenyelesaiandaripersamaanberikutini. a. 32x – 2. 3x + 1 = 27 b. 4x + 1 – 10. 2x + 1 + 16 = 0 Penyelesaian: a. 32x – 2. 3x + 1 – 27 = 0 32x – 6. 3x – 27 = 0 (3x)2 – 6. 3x – 27 = 0 Misalkan: 3x = y y2 – 6y – 27 = 0 (y – 9) (y + 3) = 0 y = 9 y = -3 Substitusikan: 3x = 9 3x = -3 3x = 32 3x = 3-1 x 2 3=3 3x = 3-1 x=2 x = -1 b. 22(x + 1) – 10. 2x + 1 + 16 = 0 22x + 2 – 10. 2x + 1 = 16 4(2x)2 – 20. 2x + 16 = 0 Misalkan 2x = p 4p2 – 20p + 16 = 0 (2p – 2) (2p – 8) = 0 p=1 p=4 Substitusikan: 2x = 1 2x = 4 x=0 x=2

HP { 2,−1 }

2x = 20

2x = 22

HP { 0,2 }