Question

若(1+根号2)^5=a+b根号2(a,b为有理数),则a+b=

请详细解答下，谢谢啦

Answer 1

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Answer 2

(1+√5)²
=1+2√5+5
=6+2√5
=a+b√5
所以a=6
b=2

Answer 3

1、
A+B
=(a²-2ab+b²)+(a²+2ab+b²)
=a²-2ab+b²+a²+2ab+b²
=2a²+2b²

2、
(B-A)/4
=[(a²+2ab+b²)-(a²-2ab+b²)]/4
=(a²+2ab+b²-a²+2ab-b²)/4
=4ab/4
=ab

3、
C=3B-2A
=3(a²+2ab+b²)-2(a²-2ab+b²)
=3a²+6ab+3b²-2a²+4ab-2b²
=a²+10ab+b²

Answer 4

解：∵(1+√2)^5=1+5√2+10(√2)^2+10(√2)^3+5(√2)^4+(√2)^5
=1+5√2+20+20√2+20+4√2
=41+29√2
又(1+√2)^5=a+b√2
∴a+b√2=41+29√2
∵a,b为有理数
∴a=41，b=29
故a+b=41+29=70。