Question

已知a²+b²-10a-6b+34,求【(a-b)÷(a+b)】÷(a²-b²)÷(ab)×(

接上a²+2ab+b²）÷（a²-ab）

Answer 1

a²+b²-10a-6b+34=0
a²-10a+25+b²-6b+9=0
(a-5)^2+(b-3)^2=0
a=5
b=3

【(a-b)÷(a+b)】÷(a²-b²)÷(ab)×(a²+2ab+b²）÷（a²-ab）

=[(a-b)/(a+b)]/[(a-b)(a+b)*ab]*(a+b)^2/a(a-b)
=(a-b)/[(a+b)*(a-b)(a+b)*ab]*(a+b)^2/a(a-b)
=(a-b)/[(a+b)^2*(a-b)*ab]*(a+b)^2/a(a-b)
=(a-b)*(a+b)^2/[(a+b)^2*(a-b)*ab*a(a-b)]
=(a-b)*(a+b)^2/[(a+b)^2*(a-b)^2*a^2b]
=1/[(a-b)*a^2b]
=1/[(5-3)*5^2*3]
=1/(2*25*3)
=1/150

Answer 2

∵a²+b²-10a-6b+34=0
∴a²-10a+25+b²-6b+9=0
∴(a-5)²+(b-3)²=0
∴(a-5)²≥0 (b-3)²≥0
∴a-5=0 b-3=0
∴a=5 b=3
然后代入求值
原式=2÷8÷16÷15×64÷10
=2÷8÷16×4×16÷15÷10
=1/150