已知:a=根号2+1分之根号2-1,b=根号2-1分之根号2+1,求a平方+b平方分之a+b+ab的值

a=√2-1/√2+1b=√2+1/√2-1求:a+b+ab/a²+b平方的值
2024-12-30 01:45:40
推荐回答(2个)
回答1:

∵a=(√2-1)/(√2+1)=(√2-1)^2/(√2+1)(√2-1)=3-2√2,
b=√2+1/√2-1=3+2√2,
a+b=6
ab=1
∴(a+b+ab)/(a²+b^2)
=(6+1)/[(a+b)^2-2ab]
=7/(36-2)
=7/34

回答2:

a=(√2-1)/(√2+1)=(√2-1)^2=3-2√2
b=(√2+1)/(√2-1)=(√2+1)^2=3+2√2

(a+b+ab)/(a^2+b^2)
=[3-2√2+3+2√2+(3-2√2)(3+2√2)]/(9-12√2+8+9+12√2+8)
=(6+9-8)/34
=7/34