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In this paper,it is shown that:if λ1,..,λ8 are nonzero real numbers,not all of the same sign,such that λ1/λ2 is irrational,then for any real numbex,η and ε＞0 the inequality,|λ1x21+λ2x22+λ3x43+…+λ8x48+η|＜ε has infinitely many solutions in positive integers x1,…,x8.