Question

寧兒吖～

請教這題🙏 看了詳解還是不太懂

SN
如右圖,甲、乙均為正方
形,其邊長分別為2a、2b,
且a>ba、b均為整數。已
知正方形甲、乙之面積相差 96,則正方形甲之
10
面積可能為何?
$825
6
24(一)
49-46=76
=765期:六
口服:13824(2)
a ² + b² = 96 ÷ 4 ÷ (-4)-EE)
1
= -6
PES-CH)(BESYN)
b
2
(a+b)=
x 972ab+b=-6
71
za
26
乙
甲
A:1000 196

Answer 1

✨ 最佳解答 ✨

Ny-Ålesund

4a^2 - 4b^2 = 96
4(a^2 - b^2) = 96
a^2 - b^2 = 24
(a - b)(a + b) = 24 = 1 × 24 = 2 × 12 = 3 × 8 = 4 × 6

(1)
a - b = 1
a + b = 24
兩式相加後發覺 a 不是正整數 --> 兩數相加後為偶數的才有可能

(2)
a - b = 2
a + b = 12
==> a = 7, b = 5 ==> 2a = 14, 2b = 4

(3)
a - b = 4
a + b = 6
==> a = 5, b = 1 ==> 2a = 10, 2b = 2

面積 = 14^2 = 196 或 10^2 = 100

寧兒吖～

會了，謝謝🙏