Sisa pembagian sukubanyak x²-6x2+3x+15 dibagi oleh (x - 2) sama dengan sisa pembagian sukubanyak x³ +x²+kx-11 dibagi oleh (x + 1). Nilai 2k adalah ....

\left \{ {\big{6x_1+3x_2=60\ \ \ \ \ \ \ \ \ \ \ } \atop \big{6x_1-2x_2=80\ /\cdot(-1)}} \right. \\\\ \left \{ {\big{6x_1+3x_2=60\ \ \ \ } \atop \big{-6x_1+2x_2=-80}} \right. \\-----------\\3x_2+2x_2=60-80\\5x_2=-20\ /:5\\\\x_2=-4\\\\6x_1+3x_2=60\ /:3\\2x_1+x_2=20\ \ \ \Rightarrow\ \ \ 2x_1+(-4)=20\ \ \ \Rightarrow\ \ \ 2x_1=24\ /:2\\\\x_1=12\\\\ \left \{ {\big{x+1=12} \atop\big {x_2=-4}} \right.

Answered by kate200468 | 2024-06-10

first let's change the "x1" to "A" Nd the "x2" to "B" __ so now the problem reads "6A + 3B = 60" And "6A - 2B= 80" we want to isolate variable. and the easiest one is the "B" by getting rid of the "A". set up a subtraction problem where you take one equation away from the other. 6a-6a=0. 3b - (-2b) = 5b and 60-80=-20. so your new equation reads 5B= -20. you wanna get B on one side so yu divide 5 on both sides giving you b= -4 or "x2"=-4. from there you can plug -4 into any one of the original equations. ex: 6A -2(-4)=80 then 6A + 8=80 then you subtract 8 from both sides because you're trying to isolate the "A" variable. which leaves you with 6A = 72. and now you wanna get"A" on one side so yu divide 6 from both sides and get A=12 or "x1"=12. do a quick check and plug in these numbers into any one of the equation.

Answered by secretlyblu | 2024-06-10

To solve the system of equations, we eliminated one variable and found x 1 ​ = 12 and x 2 ​ = − 4 . First, we adjusted the equations to add them, which eliminated x 1 ​ , allowing us to solve for x 2 ​ . Next, we substituted x 2 ​ back to find x 1 ​ .
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Answered by kate200468 | 2024-12-24

Jawaban:soal:Sisa pembagian suku banyak x³ - 6x² + 3x + 15 dibagi oleh (x - 2) sama dengan sisa pembagian suku banyak x³ + x² + kx - 11 dibagi oleh (x + 1). Cari nilai 2k. caranya:1. Cari sisa pembagian x³ - 6x² + 3x + 15 oleh (x - 2) menggunakan teorema sisa:Ganti x = 2 ke dalam suku banyak:(2)³ - 6(2)² + 3(2) + 15 = 8 - 24 + 6 + 15 = 5Sisa = 52. Cari sisa pembagian x³ + x² + kx - 11 oleh (x + 1) menggunakan teorema sisa:Ganti x = -1 ke dalam suku banyak:(-1)³ + (-1)² + k(-1) - 11 = -1 + 1 - k - 11 = -k - 11Sisa = -k - 113. Karena kedua sisa tersebut sama:5 = -k - 114. Selesaikan untuk k:k = -11 - 5 = -165. Cari nilai 2k:2k = 2(-16) = -32 Jawaban: -32

Answered by ara1412 | 2025-08-25

Penjelasan dengan langkah-langkah:Jawaban terlampir pada gambar.

Answered by arnymatematika | 2025-08-25