1) jumlah semua akar real dari x^2+2x-3 = 5/x^2+2x-7 adalah... 2) f(x)= 7+5^x-1 , g(x)= 4+ ^2logx jika (f-' . g-') (y) =3, maka y=.....

Mapel : Matematika
Tingkat : Latihan Soal Olimpiade
Bab : Fungsi

Pembahasan :
x² + 2x - 3 = 5/(x² + 2x - 7)

Misal x² + 2x - 3 = a

a = 5/(a - 4)
a² - 4a = 5
a² - 4a - 5 = 0
(a - 5)(a + 1) = 0
a = 5
a = -1

a = 5
x² + 2x - 3 = 5
x² + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = -4
x = 2

a = -1
x² + 2x - 3 = -1
x² + 2x - 2 = 0

Gunakan Teorema Vietta
X1 + X2 = -b/a
X1 + X2 = -2

Jumlah semua akarnya :
= -4 + 2 - 2
= -2 - 2
= -4