Mathematics, 15.01.2020 12:31 deanlmartin

X+y+z =4
x+y-z =2
(t kuadrat -4 =t-2

berapakah nilai t agar sistem tersebut
a. tidak memiliki penyelesaian
b. satu penyelesaian
c. tak terhingga banyak penyelesaian?

Answers: 3

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Akar akar persamaan kuadrat 2x² - 3x -1 = 0 adalah x1 dan x2. Persamaan kuadrat baru yang akar akarnya satu lebih kecil dari dua kali akar akar persamaan kuadrat di atas adalah A.x² - x - 4 = 0B.x² + 5x - 4 = 0C.x² - x + 4 = 0D.x² + x + 4 = 0E.x² - 5x - 4 = 0Jawaban : A
Penyelesaian :
Akar-akar persamaan lama :  x1 dan x2

Akar-akar persamaan baru :  xA dan xB
                                             xA = 2x1 - 1
                                             xB = 2x2 - 1
                                             xA + xB  = (2x1 - 1) + (2x2 - 1)
                                                           = 2 (x1 + x2) - 2
                                                           = 2 () - 2
                                                           = 3 - 2
                                              xA + xB = 1

                                              xA . xB = (2x1 - 1) (2x2 - 1)
                                                          = 4 x1.x2 - 2(x1 + x2) + 1
                                                          = 4.(-) - 2() + 1
                                                          = -2 - 3 + 1
                                              xA . xB = -4

Jadi persamaan kuadrat baru : x² - (xA + xB)x + xA . xB = 0
                                              x² - x - 4 = 0

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X+y+z =4
x+y-z =2
(t kuadrat -4 =t-2

berapakah nilai t agar sistem tersebut<...

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