Question

已知(a+b)的平方=3 (a-b)的平方=2 求去a方+b方,ab的值

Answer 1

(a+b)^2=a^2+2ab+b^2=3
(a-b)^2=a^2+ b^2-2ab=2
a^2+b^2=((a+b)^2+(a-b)^2)/2=5/2=2.5
ab=((a+b)^2-a^2-b^2)/2=(3-2.5)/2=0.25

Answer 2

(a+b)的平方=2 =>a^2+2ab+b^2=2 ............(1)
3 (a-b)的平方=2 =>(a-b)的平方=2/3 => a^2-2ab+b^2=2/3 ................(2)
则:(1)式减去(2)式得出:ab=1/3
则a^2+b^2=4/3