What is #(1-3sqrt7)(4-3sqrt7)#?

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Answer 1 · 2016-03-16T11:53:11

#(1-3sqrt(7))(4-3sqrt(7))=67-15sqrt(7)#

You could think that

#sqrt(7)=a#

Therefore

#(1-3sqrt(7))(4-3sqrt(7))=(1-3a)(4-3a)#

that becomes a polinomial product

#(1-3a)(4-3a)=1*4-1*3a-3a*4+(3a)^2=#
#=4-3a-12a+9a^2=4-15a+9a^2=#

Now you substitute #a# with #sqrt(7)#

#=4-15sqrt(7)+9*7=4+63-15sqrt(7)=67-15sqrt(7)#

With practice you will be able to avoid the substitution and compute the product immediately.