Đáp án+Giải thích các bước giải:
`a)ĐKXĐ:x>=0`
`E=((x+2)/((sqrtx+1)(x-sqrtx+1))-(x-sqrtx+1)/((sqrtx+1)(x-sqrtx+1)))*(4sqrtx)/3`
`E=((x+2-x+sqrtx-1)/((sqrtx+1)(x-sqrtx+1)))*(4sqrtx)/3`
`E=(sqrtx+1)/((sqrtx+1)(x-sqrtx+1))*(4sqrtx)/3`
`E=(4sqrtx)/(3(x-sqrtx+1))`
`b)E=8/9`
`<=>(4sqrtx)/(3(x-sqrtx+1))=8/9`
`<=>sqrtx/(x-sqrtx+1)=2/3`
`<=>2x-2sqrtx+2=3sqrtx`
`<=>2x-5sqrtx+2=0`
`<=>(2sqrtx-1)(sqrtx-2)=0`
`<=>[(x=4),(x=1/4):}`
`c)E=(4sqrtx)/(3(x-sqrtx+1))`
`E=4/(3(sqrtx-1+1/sqrtx))`
Áp dụng bđt cois ta có:
`sqrtx+1/sqrtx>=2`
`=>sqrtx-1+1/sqrtx>=2-1=1`
`=>3(sqrtx-1+1/sqrtx)>=3>0`
`=>E<=4/3`
Dấu "=" xảy ra khi `x=1.`
