已知x^-1+x^1=3,求x^3/2+x^-3/2的值
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已知x^-1+x^1=3,求x^3/2+x^-3/2的值
已知x^-1+x^1=3,求x^3/2+x^-3/2的值
已知x^-1+x^1=3,求x^3/2+x^-3/2的值
因为x^-1+x^1=3即1/x+x=3(1/x,x均是正数)所以x>0,所以x^1/2,x^3/2均大于0
x^-1+x^1=3
x^-1+x^1+2=3+2
(x^-1/2+x^1/2)²=5
x^-1/2+x^1/2=√5
(公式a³+b^-3=(a+b^-1)(a²-ab^-1+b^-2))
x^3/2+x^-3/2=(x^1/2+x^-1/2)(x^1+x^-1-x^1/2 × x^-1/2)
=(x^1/2+x^-1/2)(x^1+x^-1-1)
=√5×(3-1)
=2√5
答案是2√5