It is known that the sum of the two parts of the equation AX & sup2; + BX + C = 0 (a ≠ 0) is p, the sum of the squares of the two parts is Q, and the sum of the cubes of the two parts is r Write all the steps!

It is known that the sum of the two parts of the equation AX & sup2; + BX + C = 0 (a ≠ 0) is p, the sum of the squares of the two parts is Q, and the sum of the cubes of the two parts is r Write all the steps!

Let two be x1, x2
∴x1+x2=-b/a=p
x1x2=c/a
q=x1²+x2²=(x1+x2)²-2x1x2=(b²-2ac)/a²
r=x1³+x2³=(x1+x2)[(x1+x2)²-3x1x2]=-b/a(b²/a²-3c/a)
∴ar+bq+cp
=-b(b²-3ac)/a²+b(b²-2ac)/a²-bc/a
=[-b³+3abc+b³-2abc-abc]/a²
=0

If the sum of two squares of the quadratic equation AX + BX + C = 0 is p, the sum of two squares is Q, and the sum of two cubes is r, then the value of Ar + BQ + CP is A-1 b.0
If the sum of two squares of the quadratic equation AX + BX + C = 0 is p, the sum of two squares is Q, and the sum of two cubes is r, then the value of Ar + BQ + CP is A-1 b.0 C.1 D.2
2. To make the equation system 2x square + y square = 6, MX + y = 3 have a real number solution, m value a plus or minus 1, B plus or minus root sign 2, C plus or minus 3, D plus or minus root sign 3
3. The selling price of TV sets has been reduced by 10% for two consecutive times. After the reduction, the selling price of each TV set is a yuan. The original price of each TV set of the factory should be?

1. Special value method: X & # 178; - 2x + 1 = 0,1 × 2-2 × 2 + 1 × 2 = 0
2、2x²＋﹙mx-3﹚²=6
﹙m²＋2﹚x²-6mx＋3=0
36m²-12m²-24=0
m=±1
3、a/0.9²=100a/81