If #x=3^(1/3)+3^(-1/3)# then what is the value of #3x^3-9x=10#?
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"Which following pairs of atoms, have a lower electron affinity? a) Ca,K b) I,F c) Li, Ra. I seriously don't know anything about electron affinity all ik that it can buy another element"
#3(\root(3){3}+\frac{1}{\root(3){3}})^3-9(\root(3){3}+\frac{1}{\root(3){3}})=10#
Let's solve each term on the RHS of the first equation:
#3^{\frac{1}{3}}=\root(3){3}#
#3^{-\frac{1}{3}}=\frac{1}{3^{\frac{1}{3}}}=\frac{1}{\root(3){3}}#
#\therefore x=(\root(3){3}+\frac{1}{\root(3){3}})#
Plugging in that value for #x# yields:
#3(\root(3){3}+\frac{1}{\root(3){3}})^3-9(\root(3){3}+\frac{1}{\root(3){3}})=10#
That's the extent of my knowledge. I'll have someone check and add on to this answer.
#3x^3-9x=10#
Where #x=3^(1/3)+3^(-1/3)#
Of course it's answer will be zero if the equation has a solution
Then
#x^3=[3^(1/3)+3^(-1/3)]^3#
#=>[3^(1/3)]^3+[3^(-1/3)]^3+3.3^(1/3).3^(-2/3)+3.3^(2/3).3^(-1/3)#
#=>3^1+3^(-1)+3.3^(-1/3)+3.3^(1/3)#
#=>3+1/3+3(3^(1/3)+3^(-1/3))#
#=>3+1/3+3x#
Substitute the value of #x^3#in given equation
#=>3(3+1/3+3x)-9x=10#
#=>9+1+9x-9x=10#
#10=10#
#10-10=0#
