Question

se p(x²-1).(x²+1)+q(x+2)²+r(x-1)²=2x⁴-4x²+2x-9, determine o valor de q

Answer 1

p(x²-1).(x²+1)+q(x+2)²+r(x-1)²=2x⁴-4x²+2x-9

px⁴ -px² +rp(x²+4x+4)(x²-2x+1)= -4x²+2x-9

px4 -px² + ( ₁x²q + q + 4rxq + 4rq , + 4rq ) x ( x² -2x + 1 ) = 2x² - 4x² + 2x - 9

px px² + rx q - 2rx³q + rx²q + 4rx³q - 8rx²q + 4rxq + 4rx²q - 8rxq + 4rq = 2x¹ - 4x²2x - 9

px - px² + rx¹q + 2rx³q - 3rx²q - 4rxq + 4rq = 2x² 4x² 2x 9

rx q + 2rx³q - 3rx²q - 4rxq + 4rq = 2x - 4x² + 2x - 9 - px + px²

4 ( rx² + 2rx³ - 3rx² - 4rx + 4r ) q = 2x² - 4x² + 2 + px²

q = (2x⁴ -4x² +2x -9 -px⁴ +px²)/(rx⁴ +2rx³ -3rx² -4rx +4r)