已知a-b=1⼀2,a^2+b^2=1.求ab及(a^2-b^2)^2

2024-12-05 05:45:06
推荐回答(4个)
回答1:

(a-b)^2=a^2-2ab+b^2
因:a-b=1/2, a^2+b^2=1
所以:1-2ab=1/4
可得:ab=3/8

(a^2-b^2)^2
=[(a-b)(a+b)]^2
=(a-b)^2(a+b)^2 [注:(a+b)^2=a^2+2ab+b^2 ]
=1/4 x 49/16
=49/64

回答2:

a-b=1/2 (1)
a^2+b^2=1 (2)
由(2)得;(a-b)^2=1-2ab(3)
把(1)代入(3)得;:ab=3/8 (4)
由 (2)得:(a^2+b^2)^2=1^2=1
a^4+2a^2b^2+b^4=1
a^4-2a^2b^2+b^4+4a^2b^2=1
(a^2-b^2)^2=1-4a^2b^2 (5)
把(4)代入(5)得:(a^2-b^2)^2=1-4*9/64=7/16
所以:ab的值是3/8,(a^2-b^2)^2的值是7/16

回答3:

(a-b)^2=a^2-2ab+b^2
ab=1/2[a^2+b^2-(a-b)^2]
=1/2(1-1/4)
=1/2*3/4
=3/8
(a^2-b^2)^2
=[(a-b)(a+b)]^2
=(a-b)^2(a+b)^2
=(a-b)^2[(a^2+2ab+b^2]
=1/4 x (1+2*3/8)
=1/4*7/4
=7/16

回答4:

∵a-b=1/2
a^2+b^2=1
1/4=(a-b)^2=a^2+b^2-2ab=1-2ab
∴ab=3/8
又∵(a+b)^2=a^2+b^2+2ab=7/4
(a^2-b^2)^2=[(a+b)(a-b)]^2=(a+b)^2*(a-b)^2=7/4 *1/4=7/16