Question

☻

求解

√10
若 a=log
,
b=(-) log2, c = 100 log³, 1√√a² +b² + c²+2ab2bc-2ca=
100
10

Answer 1

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qn

a² + b² + c² + 2ab - 2bc - 2ca
= a² + b² + (-c)² + 2ab + 2b(-c) + 2(-c)a
= (a+b-c)²
⇒ 所求 = √(a+b-c)² = |a+b-c|

a = -3/2
b = 1/2
c = 9

⇒ 所求 = | -3/2 + 1/2 - 9 | = | -10 | = 10