Kharisma K
29 November 2023 14:00
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Kharisma K
29 November 2023 14:00
Pertanyaan
Butuh jawaban cepet
Butuh jawaban cepet
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Sumber W
Community
29 November 2023 21:44
<p>Jawaban yang tepat adalah<strong> x<sup>2</sup> - 6x + 1 = 0</strong></p><p> </p><p>Pembahasan :</p><p>2x<sup>2</sup> - 4x + 1 = 0</p><p>a = 2, b = -4 dan c = 1</p><p>Rumus ABC :</p><p>x<sub>1,2</sub> = (-b ± √(b<sup>2</sup> - 4ac)) / 2a</p><p> = (-(-4) ± √((-4)<sup>2</sup> - 4(2)(1))) / 2(2)</p><p> = (4 ± √(16 - 8)) / 4</p><p> = (4 ± √8) / 4</p><p> = (4 ± 2√2) / 4</p><p> = 2(2 ± √2) / 4</p><p> = (2 ± √2) / 2</p><p>m = (2 + √2) / 2</p><p>n = (2 - √2) / 2</p><p> </p><p>m/n = (2 + √2)/2 x 2/(2 - √2)</p><p> = (2 + √2)/(2 - √2)</p><p>n/m = (2 - √2)/2 x 2/(2 + √2) </p><p> = (2 - √2)/(2 + √2) </p><p>m/n + n/m = (2 + √2)/(2 - √2) <strong>+</strong> (2 - √2)/(2 + √2)</p><p> = [(2 + √2)(2 + √2) <strong>+</strong> (2 - √2)(2 - √2)]/[(2 - √2)(2 + √2)]</p><p> = [(4 + 4√2 + 2) <strong>+</strong> (4 - 4√2 + 2)]/4 - 2</p><p> = [4 + 4√2 + 2 <strong>+</strong> 4 - 4√2 + 2]/4 - 2</p><p> = 12/2</p><p> = 6</p><p>m/n . n/m = [(2 + √2)/(2 - √2)] . [(2 - √2)/(2 + √2)]</p><p> = [(2 + √2)(2 - √2)]/[(2 + √2)(2 - √2)]</p><p> = 1</p><p> </p><p>Rumus akar kudrat baru :</p><p>x<sup>2</sup> - (m/n + n/m)x + (m/n . n/m) = 0</p><p>x<sup>2</sup> - 6x + 1 = 0</p>
Jawaban yang tepat adalah x2 - 6x + 1 = 0
Pembahasan :
2x2 - 4x + 1 = 0
a = 2, b = -4 dan c = 1
Rumus ABC :
x1,2 = (-b ± √(b2 - 4ac)) / 2a
= (-(-4) ± √((-4)2 - 4(2)(1))) / 2(2)
= (4 ± √(16 - 8)) / 4
= (4 ± √8) / 4
= (4 ± 2√2) / 4
= 2(2 ± √2) / 4
= (2 ± √2) / 2
m = (2 + √2) / 2
n = (2 - √2) / 2
m/n = (2 + √2)/2 x 2/(2 - √2)
= (2 + √2)/(2 - √2)
n/m = (2 - √2)/2 x 2/(2 + √2)
= (2 - √2)/(2 + √2)
m/n + n/m = (2 + √2)/(2 - √2) + (2 - √2)/(2 + √2)
= [(2 + √2)(2 + √2) + (2 - √2)(2 - √2)]/[(2 - √2)(2 + √2)]
= [(4 + 4√2 + 2) + (4 - 4√2 + 2)]/4 - 2
= [4 + 4√2 + 2 + 4 - 4√2 + 2]/4 - 2
= 12/2
= 6
m/n . n/m = [(2 + √2)/(2 - √2)] . [(2 - √2)/(2 + √2)]
= [(2 + √2)(2 - √2)]/[(2 + √2)(2 - √2)]
= 1
Rumus akar kudrat baru :
x2 - (m/n + n/m)x + (m/n . n/m) = 0
x2 - 6x + 1 = 0
· 0.0 (0)
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S. Amamah
Mahasiswa/Alumni Universitas Negeri Malang
30 November 2023 06:24
<p>Jawaban: x<sup>2 </sup>- 6x + 1 = 0</p><p> </p><p>ingat!</p><p>persamaan kuadrat baru di akar -akar x1 dan x2 adalah</p><p>x<sup>2</sup> -(x1+x2)x + (x1.x2) = 0</p><p> </p><p>Diketahui: 2x<sup>2</sup> - 4x + 1 = 0 diperoleh a = 2, b = -4 dan c = 1</p><p>m + n = -b/a = -(-4)/2 = 2</p><p>m.n = c/a = 1/2 </p><p> </p><p>maka</p><p>m/n + n/m = (m.m + n.n)/m.n</p><p>= (m<sup>2</sup>+n<sup>2</sup>)/m.n</p><p>=[(m+n)<sup>2</sup>-2.mn]/m.n</p><p>= [(2)<sup>2</sup>-2.1/2]/(1/2)</p><p>= [4-1]/[1/2]</p><p>=3 x 2</p><p>= 6</p><p> </p><p>m/n x n/m = (m.n)/(n.m)</p><p>= (1/2)/(1/2) </p><p>= 1</p><p> </p><p>diperoleh:</p><p>x<sup>2</sup> -(m/n + n/m)x + (m/n x n/m) = 0</p><p>x<sup>2 </sup>- 6x + 1 = 0</p><p> </p><p>Jadi, persamaan kuadrat baru tersebut adalah x<sup>2 </sup>- 6x + 1 = 0</p>
Jawaban: x2 - 6x + 1 = 0
ingat!
persamaan kuadrat baru di akar -akar x1 dan x2 adalah
x2 -(x1+x2)x + (x1.x2) = 0
Diketahui: 2x2 - 4x + 1 = 0 diperoleh a = 2, b = -4 dan c = 1
m + n = -b/a = -(-4)/2 = 2
m.n = c/a = 1/2
maka
m/n + n/m = (m.m + n.n)/m.n
= (m2+n2)/m.n
=[(m+n)2-2.mn]/m.n
= [(2)2-2.1/2]/(1/2)
= [4-1]/[1/2]
=3 x 2
= 6
m/n x n/m = (m.n)/(n.m)
= (1/2)/(1/2)
= 1
diperoleh:
x2 -(m/n + n/m)x + (m/n x n/m) = 0
x2 - 6x + 1 = 0
Jadi, persamaan kuadrat baru tersebut adalah x2 - 6x + 1 = 0
· 0.0 (0)
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