Question

Garis y=2x+k memotong parabol y=x^2-x+3 di titik (x1,y1) dan (x2,y2) jika x1^2+x2^2=7 nilai k=

Answer 1

X^2 -x +3 = 2x + k
x^2 -x-2x + 3-k = 0
x^2 -3x +(3-k)=0

a=1 b=-3 c=(3-k)
x1 + x2 = -b/a = -(-3)/1
= 3
x1.x2 = c/a = (3-k)/1
= 3-k

x1^2 + x2^2 = 7
(x1+x2)^2 - 2.x1.x2 = 7
(3)^2 - 2(3-k) = 7
9 -6 + 2k = 7
3 + 2k = 7
2k = 7-3
2k = 4
k = 4/2 = 2