[a]=3 [b]=4 [a+b]=根下33 求[a-b]

|a-b|²+|a+b|²
=(a-b)²+(a+b)²
=a²-2ab+b²+a²+2ab+b²
=2(a²+b²)
=2(|a|²+|b|²)
代入|a|=3,|b|=4,|a+b|=根号33得
|a-b|²+33=2×(9+16)
|a-b|²=17
|a-b|=根号17

(a+b)^2=a^2+b^2+2ab=3^2+4^2+2ab=25+2ab=33,
所以2ab=8,
所以(a-b)^2=a^2+b^2-2ab=25-8=17,
所以|a-b|=根号17.

[a+b]^2+[a-b]^2=2(a^2+b^2)=2(3*3+4*4)=50

[a-b]^2=50-33=17
[a-b]=根号17