Luna M
19 September 2022 15:43
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Luna M
19 September 2022 15:43
Pertanyaan
Tentukan himpunan penyelesaian persamaan kuadrat berikut dengan cara melengkapkan kuadrat sempurna a. x² - 4x - 32 = 0 b. 2x² + 9x - 5 = 0
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2
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M. F
20 September 2022 06:56
<p>Melengkapkan kuadrat sempurna</p><p>a. x²- 4x - 32 =0</p><p>x² - 4x = 32</p><p>x²- 4x + (4/2)² = 32 + (4/2)²</p><p>x² - 4x + 4 = 32 + 4</p><p>(x - 2)² = 36</p><p>(x - 2) =±√36</p><p>(x - 2)= ±6</p><p> </p><p>diperoleh:</p><p>x<sub>1</sub> - 2 = 6 </p><p>x<sub>1</sub> = 6 + 2</p><p>x<sub>1</sub> = 8</p><p> </p><p>x<sub>2</sub> - 2 = -6 </p><p>x<sub>2</sub> = -6 + 2</p><p>x<sub>2</sub> = -4</p><p>Himpunan penyelesaian = {-4, 8}</p><p> </p><p>b.2x²+9x-5 = 0</p><p>-----------------‐‐--- (dibagi 2)</p><p>X² +9/2 x - 5/2 = 0</p><p>X² +9/2x = 5/2</p><p>X² + 9/2x + (9/4)² = 5/2 + 81/16</p><p>X² + 9/2 x + 81/16 = 121/16</p><p>(X + 9/4)² = 121/16</p><p>(X + 9/4) = ±√121/16</p><p>(X+9/4) = ± 11/4</p><p> </p><p>diperoleh:</p><p>x<sub>1</sub> + 9/4 = 11/4 </p><p>x<sub>1</sub> = 11/4 - 9/4</p><p>x<sub>1</sub> = 2/4</p><p>x<sub>1</sub> = 1/2</p><p> </p><p>x<sub>2</sub> + 9/4 = -11/4</p><p>x<sub>2</sub> = -11/4 - 9/4</p><p>x<sub>2</sub> = -20/4</p><p>x<sub>2</sub> = -5</p><p>Jadi, himpunan penyelesaian = {-5, ½}</p>
Melengkapkan kuadrat sempurna
a. x²- 4x - 32 =0
x² - 4x = 32
x²- 4x + (4/2)² = 32 + (4/2)²
x² - 4x + 4 = 32 + 4
(x - 2)² = 36
(x - 2) =±√36
(x - 2)= ±6
diperoleh:
x1 - 2 = 6
x1 = 6 + 2
x1 = 8
x2 - 2 = -6
x2 = -6 + 2
x2 = -4
Himpunan penyelesaian = {-4, 8}
b.2x²+9x-5 = 0
-----------------‐‐--- (dibagi 2)
X² +9/2 x - 5/2 = 0
X² +9/2x = 5/2
X² + 9/2x + (9/4)² = 5/2 + 81/16
X² + 9/2 x + 81/16 = 121/16
(X + 9/4)² = 121/16
(X + 9/4) = ±√121/16
(X+9/4) = ± 11/4
diperoleh:
x1 + 9/4 = 11/4
x1 = 11/4 - 9/4
x1 = 2/4
x1 = 1/2
x2 + 9/4 = -11/4
x2 = -11/4 - 9/4
x2 = -20/4
x2 = -5
Jadi, himpunan penyelesaian = {-5, ½}
· 0.0 (0)
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ARSIE J
20 September 2022 00:36
<p>Melengkapkan kuadrat sempurna</p><p>a.x²-4x-32 =0</p><p>x²-4x = 32</p><p>x²- 4x + (4/2)² = 32 + (4/2)²</p><p>x²-4x + 4 = 32 + 4</p><p>(x +2)² = 36</p><p>(X+2) =±√36</p><p>(X+2)= ±6</p><p>X1 =》 x+2= 6 </p><p> x= 6-2 =4</p><p>X2=》 x+2 = -6</p><p> x= -6-2 = -8</p><p>Himpunan penyelesaian = { x1= 4 , x2=-8}</p><p> </p><p>b.2x²+9x-5 = 0</p><p>-----------------‐‐---dibagi 2</p><p>X² +9/2 x - 5/2 = 0</p><p>X² +9/2x = 5/2</p><p>X² + 9/2x + (9/4)² = 5/2 + 81/16</p><p>X² + 9/2 x + 81/16 = 121/16</p><p>(X + 9/4)² = 121/16</p><p>(X + 9/4) = ±√121/16</p><p>(X+9/4) = ± 11/4</p><p>X1=》 x+9/4 = 11/4</p><p> x = 11/4 -9/4</p><p> x= 2/4</p><p> x= 1/2</p><p>X2=》 x+9/4= -11/4</p><p> X = -11/4 - 9/4</p><p> X = -20/4</p><p> X = -5</p><p>Jadi himpunan penyelesaian ={ x1= 1/2, x2=-5}</p><p> </p><p> </p><p> </p><p> </p>
Melengkapkan kuadrat sempurna
a.x²-4x-32 =0
x²-4x = 32
x²- 4x + (4/2)² = 32 + (4/2)²
x²-4x + 4 = 32 + 4
(x +2)² = 36
(X+2) =±√36
(X+2)= ±6
X1 =》 x+2= 6
x= 6-2 =4
X2=》 x+2 = -6
x= -6-2 = -8
Himpunan penyelesaian = { x1= 4 , x2=-8}
b.2x²+9x-5 = 0
-----------------‐‐---dibagi 2
X² +9/2 x - 5/2 = 0
X² +9/2x = 5/2
X² + 9/2x + (9/4)² = 5/2 + 81/16
X² + 9/2 x + 81/16 = 121/16
(X + 9/4)² = 121/16
(X + 9/4) = ±√121/16
(X+9/4) = ± 11/4
X1=》 x+9/4 = 11/4
x = 11/4 -9/4
x= 2/4
x= 1/2
X2=》 x+9/4= -11/4
X = -11/4 - 9/4
X = -20/4
X = -5
Jadi himpunan penyelesaian ={ x1= 1/2, x2=-5}
· 1.0 (1)
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