Question

a-b=4, ab=1/2 求a^5+b^5

Answer 1

答过的吧
解答：
已知a-b=4, ab=1/2, 求a^5+b^5

a^5+b^5
=(a^2+b^2)(a^3+b^3)-a^2b^3-a^3b^2
=(a^2+b^2)(a^3+b^3)-a^2b^2(a+b)
∵ a-b=4, ab=1/2
a²+b²=(a-b)²+2ab=16+1=17
(a+b)²=(a-b)²+4ab=16+2=18
a+b=±3√2
a³+b³=(a+b)(a²-ab+b²)=(a+b)(4-1/2)=(7/2)(a+b)

(1) a+b=3√2
原式=17*(7/2)*3√2-(1/4)*3√2=(2139√2)/4
(2) a+b=-3√2
原式=-17*(7/2)*3√2+(1/4)*3√2=-(2139√2)/4

Answer 2

(a-b)^2=a^2-2ab+b^2=(a+b)^2-4ab=16
则(a+b)^2=18 a+b=3根号2 或a+b=-3根号2.

a^5+b^5
=(a+b)(a^4-a^3b+a^2b^2-ab^3+b^4)
=(a+b)((a^3(a-b)+a^2b^2-b^3(a-b))
=(a+b)((a^3-b^3)(a-b)+a^2b^2)
=(a+b)((a-b)^2(a^2+ab+b^2)+a^2b^2)
=(a+b)(16(a^2+ab+b^2)+a^2b^2)
=(a+b)(16((a-b)^2+3ab)+a^2b^2)
=(a+b)(16(16+3/2)+a^2b^2)
=(a+b)(16^2+24+1/4)
=(256+24+1/4)(a+b)
=(280+1/4)(a+b)
=(280+1/4)*(3根号2)或-(280+1/4)*(3根号2).

Answer 3

a^2+b^2=17,a^4+b^4=288.5,a+b=3*根号2，
a^5+b^5=280.25*3*根号2

Answer 4

a=b+4,带进去（b+4）*b=1/2,求出a= b=

Answer 5

画坐标图啊，当a=4，则b=0；当a=5，则b=1。实际上a-b=4，是45度角，所以a=b，接下来你懂个的啊！慢慢思考哦！