Consider the equation \(\displaystyle{\left({{\log}_{{2}}{x}}\right)}^{{2}}-{4}{{\log}_{{2}}{x}}-{\left({m}^{{2}}+{2}{m}+{13}\right)}={0}\). Let the real

Lucian Ayers

Lucian Ayers

Answered question

2022-03-26

Consider the equation (log2x)24log2x(m2+2m+13)=0. Let the real roots of the equation be x1,x2 such that x1<x2. Find the sum of maximum value of x1 and minimum value of x2.

Answer & Explanation

tabido8uvt

tabido8uvt

Beginner2022-03-27Added 16 answers

Step 1
x2=22+m2+2m+17=22+(m+1)2+1622+4=64.
Step 2
x1=22m2+2m+17=22(m+1)2+16224=14.
The equality in the both cases occurs for m=1, which gives the answer: 6414.

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