Question

已知(a+b)=7,(a-b)的平方=4,求a的平方加b的平方和ab的值

Answer 1

2(a^2+b^2)
=(a+b)^2-(a-b)^2
=7-4
=3
a^2+b^2
=3÷2
=1.5

2ab
=(a+b)^2-(a^2+b^2)
=7-1.5
=5.5
ab
=5.5÷2
=11/4
或
∵（a+b）² =7 ； （ a-b）²=4
∴（a+b）² +（ a-b）²
（a²+2ab+b²）+(a²-2ab+b²)=7+4
2a²+2b²=11;
∴2(a²+b²)=11
a²+b²=11/2

Answer 2

解析
a²+b²=1/2[(a+b)²+(a-b)²]
=1/2(a²+b²+2ab+a²+b-2ab)
=1/2(2a²+2b²)
=1/2*(7+4)
=11/2

ab=1/4[(a+b)²-(a-b)²]
=1/4(a²+2ab+b²-a²+2ab-b²)
=1/4(7-4)
=3/4

楼下的题目都不对额