1. 9 x² – 4 =0 (3x+……) (…..-……) = 0 atau atau jdi himpunan penyelesaiannya adalah (…..) 2. 2x² +5 – 3 =0 (2x-…..). (x+…….)=0 atau atau jdi himpunan penyelesaiannya adalah (…….) 3. 4a (a + 1)=15 ……+ ………=0 atau atau jdi himpunan penyelesaiannya adalah(….) 4. m² – m – 6 = 0 (m+……) (…..-……)=0 atau atau jdi himpunan penyelesaiannya adalah (…..)

1. 9 x² – 4 =0(3x+……) (…..-……) = 0
atau
jdi himpunan penyelesaiannya adalah (…..)

2. 2x² +5 – 3 =0
(2x-…..). (x+…….)=0
atau
atau
jdi himpunan penyelesaiannya adalah (…….)

3. 4a (a + 1)=15
……+ ………=0
atau
atau
jdi himpunan penyelesaiannya adalah(….)

4. m² – m – 6 = 0
(m+……) (…..-……)=0
atau
atau
jdi himpunan penyelesaiannya adalah (…..)

Jawab:
(1.) 9x² – 4 = 0
(3x + 2)(3x-2) = 0
Hp = {-⅔, ⅔}

(2.) 2x² + 5x – 3 = 0
(2x-1) (x+3) = 0
Hp = {½, -3}

(3.) 4a(a+1) = 15
(2a-3) (2a+5) = 0
Hp = {³/₂, -⁵/₂}

(4.) m² – m – 6 = 0
(m + 2)(m – 3) = 0
Hp = {-2, 3}

Penjelasan :

(1.) 9x² – 4 = 0
(3x)² – 2² = 0
a² – b² = (a+b)(a-b)
(3x + 2)(3x-2) = 0
Hp = {-⅔, ⅔}

(2.) 2x² + 5x – 3 = 0
a = 2
x² + 5x – 3(2) =0
x² + 5x – 6 = 0
b = 5, c = -6
b+c = 5, bc = -6
-1+6 = 5, -1(6) = -6
b = -1, c = 6
¹/ₐ (ax+b)(ax+c) = 0
½ (2x-1) (2x+6) = 0
(2x-1) (²/₂x+⁶/₂) = 0
(2x-1) (x+3) = 0
Hp = {½, -3}

(3.) 4a(a+1) = 15
a(a+1) = ¹⁵/₄
a² + a = ¹⁵/₄
a² + a + (½)² = ¹⁵/₄ + (½)²
a² + 2a(½) + (½)² = ¹⁵/₄ + ¼
(a + ½)² = ¹⁶/₄
(a + ½)² = 4
a + ½ = ±√4
a + ½ = ±2
a = ±2 – ½
Hp = {2 – ½, -2 – ½}
Hp = {⁴/₂ – ½, -⁴/₂ – ½}
Hp = {³/₂, -⁵/₂}
(2a-3) (2a+5) = 0
Hp = {³/₂, -⁵/₂}

(4.) m² – m – 6 = 0
ab = -6, a + b = -1
2(-3) = -6, 2 – 3 = -1
a = 2, b = -3
(m + a)(m + b) = 0
(m + 2)(m – 3) = 0
Hp = {-2, 3}

 

 

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