换元法解f(2x+1)=x²-2x,求f(2√2+1)和f(2√2+3)

题目

换元法解f(2x+1)=x²-2x,求f(2√2+1)和f(2√2+3)

答案

(1)
令x=√2
f(2√2+1)=2-2√2
(2)
令x=√2+1,f(2x+1)=f(2√2+3)
x-2=√2+1
f(2x+1)=x(x-2)=(√2+1)(√2-1)=1;