Question

QUIZ (1335)
Materi: Operasi Hitung

Jika [tex] \rm x = 2p - 4q [/tex] dan [tex] \rm y = -p + 2q [/tex], maka nilai dari [tex] \rm \dfrac{ 2x^2-3xy+y^2 }{ x^2-y^2} [/tex] adalah...
A. -3
B. 3
C. 5
D. 10​

Answer 1

Verified answer

Jawaban:

Aljabar

[tex]x = 2p - 4q \\ y = - p + 2q[/tex]

[tex] \frac{2 {x}^{2} - 3xy + {y}^{2} }{ {x}^{2} - {y}^{2} } = \frac{(x - y)(2x - y)}{(x + y)(x - y)} = \frac{2x - y}{x + y} \\ [/tex]

[tex] \frac{2x - y}{x + y} = \frac{2(2p - 4q) - ( - p + 2q)}{(2p - 4q) + ( - p + 2q)} \\ \frac{4p - 8q + p - 2q}{2p - 4q - p + 2q} \\ \frac{5p - 10q}{p - 2q} = \frac{5(p - 2q)}{(p - 2q)} = 5[/tex]

Answer 2

Jawab:
C.  =  5

Penjelasan:
Diketahui:
x = 2p-4q
y = -p+2q

2x² - 3xy + y²
= 2x² - 2xy - xy + y²
= (2x-y)(x-y)

x² - y² = (x+y)(x-y)

(2x² - 3xy + y²) ÷ (x² - y²)
= (2x-y)(x-y) ÷ [(x+y)(x-y)]
= (2x-y) ÷ (x+y)
= (2(2p-4q)-(-p+2q)) ÷ (2p-4q-p+2q)
= (4p-8q+p-2q) ÷ (2p-4q-p+2q)
= (5p-10q) ÷ (p-2q)
= (5(p-2q)) ÷ (p-2q)
= 5

(xcvi)