jika x1 dan x2 akar akar PK 2xpangkat 2+3x-5=0tentukan x1pangkat2+x2pangkat 2

Mapel : Matematika
Kelas : X SMA
Bab : Persamaan Kuadrat

Pembahasan :
2x² + 3x - 5 = 0

Gunakan Teorema Vietta
X1 + X2 = -b/a
X1 + X2 = -3/2

X1 . X2 = c/a
X1 . X2 = -5/2

X1² + X2² = (X1 + X2)² - 2X1 . X2
X1² + X2² = (-3/2)² - 2(-5/2)
X1² + X2² = 9/4 + 5
X1² + X2² = 29/4
X1² + X2² = 7(1/4)

[tex] 2x^{2} + 3x - 5[/tex]
x1 + x2 = -b/a = - 3/2
x1.x2 = c/a = - 5/2

Dit = [tex] x_1^{2}+ x_2^{2} [/tex]

[tex] x_1^{2}+ x_2^{2} [/tex] = [tex] (x_1+x_2)^{2}-2x_1.x_2 [/tex]

[tex] x_1^{2}+ x_2^{2} [/tex] = [tex] (-3/2)^{2}-2.(-5/2) [/tex]

[tex] x_1^{2}+ x_2^{2} [/tex] = 9/4 + 5

[tex] x_1^{2}+ x_2^{2} [/tex] = 29/4