Áp dụng BĐT Bu-nhi-a ta có:

\(\sqrt{a^2+1}=\sqrt{a^2+\dfrac{1}{3}+\dfrac{1}{3}+\dfrac{1}{3}}=\dfrac{1}{2}\sqrt{4\left(a^2+\dfrac{1}{3}+\dfrac{1}{3}+\dfrac{1}{3}\right)}\)

\(\ge\dfrac{1}{2}\sqrt{\left(a+\dfrac{1}{\sqrt{3}}.3\right)^2}=\dfrac{1}{2}\sqrt{\left(a+\sqrt{3}\right)^2}=\dfrac{a+\sqrt{3}}{2}\left(a>0\right)\)

Tương tự ta cũng có: \(\dfrac{b}{\sqrt{b^2+1}}\le\dfrac{2b}{b+\sqrt{3}}\)

\(\dfrac{c}{\sqrt{c^2+1}}\le\dfrac{2c}{c+\sqrt{3}}\)

=> \(\dfrac{a}{\sqrt{a^2+1}}+\dfrac{b}{\sqrt{b^2+1}}+\dfrac{c}{\sqrt{c^2+1}}\)

\(\le2\left(\dfrac{a}{2a+b+c}+\dfrac{b}{2b+a+c}+\dfrac{c}{2c+a+b}\right)\) (1)

Áp dụng BĐT phụ: \(\dfrac{1}{4}\left(\dfrac{1}{x}+\dfrac{1}{y}\right)\ge\dfrac{1}{x+y}\) ta có:

\(\dfrac{a}{2a+b+c}+\dfrac{b}{2b+a+c}+\dfrac{c}{2c+a+b}\)

\(=\dfrac{a}{\left(a+b\right)+\left(a+c\right)}+\dfrac{b}{\left(a+b\right)+\left(b+c\right)}+\dfrac{c}{\left(a+c\right)+\left(b+c\right)}\)

\(\le\dfrac{1}{4}\left(\dfrac{a}{a+b}+\dfrac{a}{a+c}+\dfrac{b}{a+b}+\dfrac{b}{b+c}+\dfrac{c}{a+c}+\dfrac{c}{b+c}\right)\)

\(=\dfrac{1}{4}\left(\dfrac{a+c}{a+c}+\dfrac{b+a}{a+b}+\dfrac{c+b}{b+c}\right)=\dfrac{3}{4}\) (2)

Từ (1); (2)

=> \(\dfrac{a}{\sqrt{a^2+1}}+\dfrac{b}{\sqrt{b^2+1}}+\dfrac{c}{\sqrt{c^2+1}}\le2.\dfrac{3}{4}=\dfrac{3}{2}\left(đpcm\right)\)

Dấu = xảy ra <=> \(a=b=c=\dfrac{1}{\sqrt{3}}\)

Rốt cuộc cái đề nào đúng????

PTHH: XO + H₂SO₄ --> XSO₄ + H₂O
(mol)......x...........x..................x...........x
=> \(m_{H_2SO_4}=98x\) (g)

\(m_{XO}=x\left(X+16\right)\) g

\(m_{XSO_4}=x\left(X+96\right)\) g

=> \(m_{dd.H_2SO_4}=98x:20\%=490x\) (g)

=> m_{dd sau p/ứ} = \(m_{XO}+m_{dd.H_2SO_4}\)

\(=x\left(X+16\right)+490x=x\left(X+506\right)\) (g)

Mà \(m_{XSO_4}=22,6\%.\) m_{dd sau p/ứ}

=> \(x\left(X+96\right)=0,226x\left(X+506\right)\)

=> \(X+96=0,226X+114,356\)

=> \(0,774X=18,356\)

=> \(X\approx24\left(Mg\right)\)

Vậy ..........................

=>

TRANSFORMATION

1) MARY SINGS BETTER THAN HER ELDER SISTER DOES.

=> MARY IS a better singer than her elder sister

2) HE SINGS WELL AND PLAYS THE GUITAR WELL.

=> HE BOTH sings and plays guitar well

3) MY YOUNGER BROTHER FINALLY MANAGED TO GET THE JOB.

=> MY YOUNGER BROTHER WAS finally able to get the job.

4) LIZ IS A BETTER PIANIST THAN MAI.

=> MAI DOES not play piano as well as Liz

5) SHE IS ANNOYED BECAUSE HER HUSBAND OFTEN SMOKES IN THE HOME.

=> SHE OBJECTS to her husband smoking in the house

Cmt đầu - chúc mi đc gải tán nhé Như Khương Nguyễn