Using Furuta's inequality, we can get that if $10,A_2\>B>0$ and $A_1^t\natural _{\frac{1-t}{p-t}}A_2^p\ (B^r{A_2}^pB^r)^{\frac{\a+2r}{p+2r}}.$$ holds for any $0\<\a\<\min \{2p-1,t\}$ and $ r\>0$. We can also get that if $1\0,A_2\>B>0$ and $A_1^t\natural _{\frac{2p-t}{p-t}}A_2^p\ (B^r{A_2}^pB^r)^{\frac{\a+2r}{p+2r}}.$$ holds for any $0\<\a\<2p$ and $ r\>0$.