Re: [中學] 面積求解
: 如上，欲求正方形面積
: 同學的暑假作業，但小弟我實在毫無頭緒啊
: 感覺根本無法解QQ
: 煩請各位神人解答了
: -----
如果, 正方形邊和兩軸平行, 對角線是 y=x+1, 另外兩角在拋物線上這樣的話
令在拋物線上那兩點是 (p,-2p^2+2), (q,-2q^2+2)
那麼 (p,-2q^2+2) 和 (q,-2p^2+2) 在 y=x+1 上
故 {-2q^2+2 = p+1
{-2p^2+2 = q+1
兩式相減得 2(p^2-q^2) = p-q, 因為 p-q 為正方形邊長不為零故約去得 2(p+q) = 1
代回上面任一式化簡可得 4p^2-2p-1=0 (或是 q, 式子相同)
解得 p,q = (1±√5)/4
於是邊長是這兩根相減為 (√5)/2, 平方得正方形面積為 5/4 #
--
'You've sort of made up for it tonight,' said Harry. 'Getting the
sword. Finishing the Horcrux. Saving my life.'
'That makes me sound a lot cooler then I was,' Ron mumbled.
'Stuff like that always sounds cooler then it really was,' said
Harry. 'I've been trying to tell you that for years.'
-- Harry Potter and the Deathly Hollows, P.308
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