Question

Tentukan nilai r pada persamaan bentuk aljabar (2x+3y)(px+qy)=rx²+23xy+12y²

Answer 1

(2x + 3y)(px + qy) = rx² + 23xy + 12y²
=> 2px² + 2qxy + 3pxy + 3qy² = rx² + 23xy + 12y²
=> 2px² + (3p+2q)xy + 3qy² = rx² + 23xy + 12y²
Maka:
(1) 2p = r  (2) 3p + 2q = 23 (3) 3q = 12 --> q = 12/3 = 4
=> 3p + 2q = 23
=> 3p + 2x4 = 23
=> 3p = 23 - 8 = 15
=> p = 15/3 = 5

=> r = 2p
=> r = 2x5 = 10