Question

化简求值。（根号a+根号b）²-（根号a-根号b）²，其中a=3，b=4

Answer 1

解：
原式=(√a+√b)²-(√a-√b)²
=[(√a+√b)+(√a-√b)][(√a+√b)-(√a-√b)]
=(√a+√b+√a-√b)(√a+√b-√a+√b)
=2√a×2√b
=4√(ab)
=4×√(3×4)
=4×√12
=4×2√3
=8√3

Answer 2

解：原式=(√a+√b)²-(√a-√b)²
=[(√a+√b)+(√a-√b)][(√a+√b)-(√a-√b)]
=(√a+√b+√a-√b)(√a+√b-√a+√b)
=2√a×2√b
=4√(ab)
所以，当a=3，b=4时
原式=4×√(3×4)=4×√12=4×2√3=8√3