Question

(a+ b)平方=7,(a-b)平方=3 求a四次方+ b四次方

尽快作答

Answer 1

(a+b)^2=7
a^2+b^2+2ab=7①
(a-b)^2=3
a^2+b^2-2ab=3②
①+②，得2a^2+2b^2=10→a^2+b^2=5
①-②，得4ab=4→ab=1
(a^2+b^2)^2
=a^4+b^4+2a^2b^2
a^4+b^4=(a^2+b^2)^2-2a^2b^2
=(5)^2-2(ab)^2
=5^2-2(1^2)
=23

Answer 2

（两式相加除以2）的平方减去（两式相减除以4）的平方的2倍=23

Answer 3

(a+b)^2=7
a^2+2ab+b^2=7①

(a-b)^2=3
a^2-2ab+b^2=3②

①+②
2a^2+2b^2=10
a^2+b^2=5
ab=1

(a^2+b^2)^2=25
a^4+2(ab)^2+b^4=25
a^4+b^4=23

Answer 4

a^4+b^4=(a^2+b^2)^2-2a^2b^2
(a+b)^2-(a-b)^2=4ab=4 ab=1 a^2b^2=1 2a^2b^2=2
(a+b)^2+(a-b)^2=2(a^2+b^2)=10 (a^2+b^2)^2=25
a^4+b^4=(a^2+b^2)^2-2a^2b^2=23