Question #ff941
1 Answer
Explanation:
Using
#sqrt(3)^3+sqrt(3)^2+7=A(sqrt(3)^2+9)+B#
#B=10+3sqrt(3)#
#x^3+x^2+7=A(x^2+9)+10+3sqrt(3)# With
#x=0#
#7=9A+10+3sqrt(3)#
#A=(7-10-3sqrt(3))/9=-(1+sqrt(3))/3#
#(x^3+x^2+7)/(x^2+9)^2=(-(1+sqrt(3))/3)/(x^2+9)+(10+3sqrt(3))/(x^2+9)^2=-(1+sqrt(3))/(3(x^2+9))+(10+3sqrt(3))/(x^2+9)^2#
Using
#(-sqrt(3))^3+(-sqrt(3))^2+7=A((-sqrt(3))^2+9)+B#
#B=10-3sqrt(3)#
#x^3+x^2+7=A(x^2+9)+10-3sqrt(3)# With
#x=0#
#7=9A+10-3sqrt(3)#
#A=(7-10+3sqrt(3))/9=(-1+sqrt(3))/3#
#(x^3+x^2+7)/(x^2+9)^2=((-1+sqrt(3))/3)/(x^2+9)+(10-3sqrt(3))/(x^2+9)^2=(-1+sqrt(3))/(3(x^2+9))+(10-3sqrt(3))/(x^2+9)^2#