那位可以帮我解一道数学题,已知函数f(x)满足:f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y) (x ,y∈R),把xy值代0,为什么不能得f(0)=0
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![那位可以帮我解一道数学题,已知函数f(x)满足:f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y) (x ,y∈R),把xy值代0,为什么不能得f(0)=0](/uploads/image/z/6933876-60-6.jpg?t=%E9%82%A3%E4%BD%8D%E5%8F%AF%E4%BB%A5%E5%B8%AE%E6%88%91%E8%A7%A3%E4%B8%80%E9%81%93%E6%95%B0%E5%AD%A6%E9%A2%98%2C%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%E6%BB%A1%E8%B6%B3%EF%BC%9Af%EF%BC%881%EF%BC%89%3D1%EF%BC%8F4%2C4f%28x%29f%28y%29%3Df%28x%2By%29%2Bf%28x-y%29+%28x+%2Cy%E2%88%88R%EF%BC%89%2C%E6%8A%8Axy%E5%80%BC%E4%BB%A30%2C%E4%B8%BA%E4%BB%80%E4%B9%88%E4%B8%8D%E8%83%BD%E5%BE%97f%EF%BC%880%EF%BC%89%3D0)
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