还有其他的答案..唔该

还有其他的答案..唔该

13.y = 4cosx - 3sin²x + 2 = 4cosx - 3(1-cos²x)+2 = 3cos²x + 4cosx - 1= 3(cosx + 2/3)² - 13/9因为 cosx∈[-1,1],所以当cosx + 2/3 = 0 时 y 取到最小值-13/19,当cosx = 1时 y 取到最大值 3(1+2/3)² - 13/9 = 62/9.14.由 a(n+1) - an = 2n - 1 得:a2 - a1 = 1a3 - a2 = 3a4 - a3 = 5.an - a(n-1) = 2(n-1) - 1等式两端分别相加得:an - a1 = 1+3+5+.+2(n-1)-1 = 2(n-1)(n-1)/2 = (n-1)² 所以 an= (n-1)² + a1 = (n-1)² +2.15.当n=1时,左式 = 1+ 3/1 = 4 = 2² = (1+1)² = 右式.设n = k时原式成立,即 ( 1+ 3/1)( 1+5/4).[1+(2k+1)/k²] = (k + 1)².当n = k+1 时,( 1+ 3/1)( 1+5/4).[1+(2k+1)/k][1+(2(k+1)+1)/(k+1)²]= (k + 1)² [1+(2(k+1)+1)/(k+1)²]= (k + 1)² + 2(k + 1) +1 = (k + 2)² = [(k + 1) + 1]².所以 n = k+1时原式成立.所以原式当n为正整数时成立.11.令 a = x^(1/2),则 1/a = x^(-1/2).由已知得 a + 1/a = 3.两边平方得:a^2 + 1/a^2 + 2 = 9.所以有:a^2 + 1/a^2 = 7.两边再平方

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