COMPACT (Number System)

1) If x= 106 then x(x²-3x +3)=?.       1157626

2) If x=99 then x(x²+12x+48)=?.                                     1092663

3) 1/(³√25 - ³√5 +1) = A ³√25+ B ³√5 + C. Then A+ B+ C =?                          1/3

4) 1/(³√9 - ³√3 +1) = A ³√9+ B ³√3+ C. Then A+ B+ C =?                             1

5) If x= 1/(7+ 4 √3) = y= 1/7- 4 √3, then 1/(x+1) + 1/(y+1) =?                          1

6) x= (√3 + √2)⁻³, y=(√3 - √2)⁻³ then find (x +1)⁻¹ + (y+1)⁻¹=?.                             1

7) x= 7+ 4 √3, x + 1/x =?.                     14

8) If x=14 then find x⁵- 15x⁴ + 15x³ - 15x² +15x.                                   14

9) If x=12 then find x⁶ - 13x⁵+13x⁴ -13x³ + 15x² -13x+5.                                     281

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