Question 198236
# 1


Is the expression {{{root(12,(-10)^12)}}}??? If so, then {{{root(12,(-10)^12)=10}}}



On the other hand, if the expression is {{{(root(12,-10))^12}}}, then result is NOT a real number. Why? You CANNOT take an even root of a negative number and get a real number (eg you can't take the square root of -2).


<hr>


# 2


You are correct. {{{(9x^8-7)*(x^9-5)=9x^17-7x^9-45x^8+35}}}



<hr>


# 3





From {{{12x^2-8x+7}}} we can see that {{{a=12}}}, {{{b=-8}}}, and {{{c=7}}}



{{{D=b^2-4ac}}} Start with the discriminant formula.



{{{D=(-8)^2-4(12)(7)}}} Plug in {{{a=12}}}, {{{b=-8}}}, and {{{c=7}}}



{{{D=64-4(12)(7)}}} Square {{{-8}}} to get {{{64}}}



{{{D=64-336}}} Multiply {{{4(12)(7)}}} to get {{{(48)(7)=336}}}



{{{D=-272}}} Subtract {{{336}}} from {{{64}}} to get {{{-272}}}



Since the discriminant is less than zero, this means that there are two complex solutions.



In other words, there are no real solutions.



You got the right discriminant value, but you forgot to mention what that meant in terms of the number of solutions.



<hr>


# 4


You are correct, {{{a^2+6a+9}}} factors to {{{(a+3)^2}}}.



You can verify the answer by 


a) Graphing {{{a^2+6a+9}}} and {{{(a+3)^2}}} on the same grid. You'll see that they are the same graph, or...


b) You can FOIL {{{(a+3)^2}}} to get {{{a^2+6a+9}}}