bài tập toán

Question

Rút gọn các biểu thức sau (với a>0,b>0a>0,b>0):

a) 5√a−4b√25a3+5a√16ab2−2√9a;5a−4b25a3+5a16ab2−29a;

b) 5a√64ab3−√3⋅√12a3b3+2ab√9ab−5b√81a3b.

Answer 1

a) Ta có:

5√a−4b√25a3+5a√16ab2−2√9a5a−4b25a3+5a16ab2−29a

=5√a−4b√52.a2.a+5a√42.b2.a−2√32.a=5a−4b52.a2.a+5a42.b2.a−232.a

=5√a−4b√(5a)2.a+5a√(4b)2.a−2√32.a=5a−4b(5a)2.a+5a(4b)2.a−232.a

=5√a−4b.5a√.a+5a.4b√a−2.3√a=5a−4b.5a.a+5a.4ba−2.3a

=5√a−20ab√a+20ab√a−6√a=5a−20aba+20aba−6a

=(5√a−6√a)+(−20ab√a+20ab√a)=(5a−6a)+(−20aba+20aba)

=(5−6)√a=−√a=(5−6)a=−a

b) Ta có:

5a√64ab3−√3.√12a3b3+2ab√9ab−5b√81a3b5a64ab3−3.12a3b3+2ab9ab−5b81a3b

=5a√82.b2.ab−√3.√22.3.(ab)2.ab=5a82.b2.ab−3.22.3.(ab)2.ab

+2ab√32.ab−5b√92.a2.ab+2ab32.ab−5b92.a2.ab

=5a√(8b)2.ab−√3.√(2ab)2.3.ab+2ab√32.ab=5a(8b)2.ab−3.(2ab)2.3.ab+2ab32.ab

−5b√(9a)2.ab−5b(9a)2.ab

=5a.8b√ab−√3.2√3ab√ab+2ab.3√ab=5a.8bab−3.23abab+2ab.3ab

−5b.9a√ab−5b.9aab

=40ab√ab−2.3ab√ab+6ab√ab−45ab√ab=40abab−2.3abab+6abab−45abab

=40ab√ab−6ab√ab+6ab√ab−45ab√ab=40abab−6abab+6abab−45abab

=40ab√ab−45ab√ab=40abab−45abab

=(40−45)√ab=(40−45)ab

=−5ab√ab=−5abab.