Question

Diketahui garis 4x - ay = 5 dan 3x + ( a + 1 )y = 10 saling tegak lurus. Tentukan
nilai a .

Answer 1

Karena te gak lurus berarti (m1)(m2) = -1
m1 misal utk garis 4x -ay =5
ay = 4x - 5
y = 4x/a -5/a
gradien terdapan di depan koefisien x jadi m1 = 4/a
m2 misal utk garis 3x + (a+1)y=10
(a+1)y = 10-3x
y = -3x/(a+1) +10/(a+1)
gradiennya = m2 = -3/(a+1)
m1.m2 = -1
(4/a) (-3/a+1) =-1
-12/(a)(a+1) =-1
a(a+1) = 12
a^2 + a - 12 = 0
(a-3)(a+4) = 0
a=3 atau a=-4