Question

Persamaan 2x²-4x-k+1=0 mempunyai akar akar m dan n jika m²-n²=6 hitunglah 2k+3

Jelasin dongg... please...

Answer 1

Persamaan = 2x^2 - 4x + (-k+1)

m+n = -b/a
= 4/2 = 2

m.n = c/a
= (-k+1)/2

m^2 + n^2 = (m+n)^2-2.mn
= (2)^2 - 2(-k+1/2)
= 4 + k -1
=3+ k

Lalu substitusikan

(m^2-n^2) + (m^2+n^2) =3+k + 6
2m^2 = 9 + k
m^2 = 9+k/2

substitusikan

Jadinya =

9+k/2 - n^2 = 6
9+k-12/2 = n^2
-3+ k/2 = n^2

subztitusi lagi

9+k-3+k/2 =4 -2(mn)
6 +2k = 8-4mn
-2 + 2k = -4mn
-2+2k = 4k-4
2 = 2k
k= 1

2k +3 = 2(1) + 3 = 5

Kalo ada yang kurang.jelas komen aja