Question

-unknownnn-

求詳解 ans:1,4

7. 若 a,b,c 都是正數,且9°=15°=25°,則下列哪些選項是正確的?
12 1
(1) ab+bc = 2ac(2) ab+bc = ac (3)
C b a
22 1
-=
C
2-a
110
+
b
(4)
(5) b² = ac
O

Answer 1

✨ 最佳解答 ✨

qn

9=15^(b/a)
25=15^(b/c)
9×25=15²=15^[(b/a)+(b/c)]
(b/a)+(b/c)=2
(1/a)+(1/c)=2/b → (4) ✓
同乘以abc → bc+ab=2ac → (1) ✓

ab+bc=2ac>ac → (2) ✕

(2/c)-(4/b)=-2/a
(2/c)-(1/b)=(3/b)-(2/a)≠2/a → (3) ✕

ac=b(a+c)/2≠b² → (5) ✕