Question

已知a+b=5,ab=3,求下列各式的值(1)(a-b)^2(2)a^2+b^2(3)a^4+b^4

Answer 1

1.(a-b)^2
=(a+b)^2-4ab
=25-12
=23

2.a^2+b^2
=(a+b)^2-2ab
=25-6
=19

3.a^4+b^4
=(a^2+b^2)-2a^2b^2
=361-2*9
=361-16
=343

Answer 2

1.
(a-b)²=a²-2ab+b²=a²+2ab+b²-4ab=(a+b)²-4ab=5²-12=13
2.
a²+b²=(a+b)²-2ab=5²-6=19
3.
a^4+b^4=(a²+b²)²-2a²b²=19²-2×3²=343