Do a, b, c là các số dư

=>a, b, c >0

=>a+b+c>0 và \(\dfrac{1}{a}\)+\(\dfrac{1}{b}\)+\(\dfrac{1}{c}\)>0

Áp dụng bất đẳng thức Côsi ta có :

a+b+c \(\ge\)3\(\sqrt[3]{abc}\)

\(\dfrac{1}{a}\)+\(\dfrac{1}{b}\)+\(\dfrac{1}{c}\)\(\ge\)3\(\sqrt[3]{\dfrac{1}{abc}}\)

=> (a+b+c)(\(\dfrac{1}{a}\)+\(\dfrac{1}{b}\)+\(\dfrac{1}{c}\))\(\ge\)3\(\sqrt[3]{abc}\).3\(\sqrt[3]{\dfrac{1}{abc}}\)

=> (a+b+c)(\(\dfrac{1}{a}\)+\(\dfrac{1}{b}\)+\(\dfrac{1}{c}\))\(\ge\)9\(\sqrt[3]{abc\dfrac{1}{abc}}\)

=> (a+b+c)(\(\dfrac{1}{a}\)+\(\dfrac{1}{b}\)+\(\dfrac{1}{c}\))\(\ge\)9

Hay P\(\ge\)9

Dấu "=" xảy ra <=> a=b=c

Ta có: \(\dfrac{x^2+2x-1}{\left(x-1\right)\left(x^2+1\right)}\)=\(\dfrac{a}{x-1}\)+\(\dfrac{bx+c}{x^2+1}\)

<=>\(\dfrac{x^2+2x-1}{\left(x-1\right)\left(x^2+1\right)}\)=\(\dfrac{a\left(x^2+1\right)+\left(bx+c\right)\left(x-1\right)}{\left(x-1\right)\left(x^2+1\right)}\)

=>a(x²+1)+(bx+c)(x-1)=x²+2x-1

<=>ax²+a+bx²-bx+cx-c=x²+2x-1

<=>(a+b)x²+(c-b)x-(c-a)=x²+2x-1

=>\(\left\{{}\begin{matrix}a+b=1\\c-b=2\\c-a=1\end{matrix}\right.\)

<=>\(\left\{{}\begin{matrix}a+b=1\\b=c-2\\a=c-1\end{matrix}\right.\)

<=>\(\left\{{}\begin{matrix}c-1+c-2=1\\b=c-2\\a=c-1\end{matrix}\right.\)

<=>\(\left\{{}\begin{matrix}c=2\\b=0\\a=1\end{matrix}\right.\)

Vậy a=1,b=0,c=2

Read the following passage and mark the letter A, B, C or D to indicate the correct answer to each of the questions from 36 to 42.

Scientists have discovered the bones of what may be the largest meat-eating dinosaur ever to walk the earth. The discovery was made by a team of researchers from Argentina and North America in Patagonia, a desert on the eastern slopes of the Andes in South America. Besides the interesting fact that the dinosaur was huge and horrifying, it is even more astounding that the bones of a number of the dinosaurs were found together. This discovery challenges the prior theory that the biggest meat-eaters lived as loners and instead indicates that they may have lived and hunted in packs. The Tyrannosaurus Rex lived in North America and was believed to hunt and live alone.

The newly discovered meat-eater appears to be related to the Giganotosaurus family, being as closely related to it as a fox would be to a dog. It is actually not of the same family at all as the Tyrannosaurus Rex, being as different from it as a cat is from a dog.

The fossilized remains indicate that the animals lived about 100 million years ago. With needle-shaped noses and razor sharp teeth, they were larger than the Tyrannosaurus Rex, although their legs were slightly shorter, and their jaws were designed to be better able to dissect their prey quickly and precisely.

Question 42: The author states that the newly discovered meat-eating dinosaur is   ________.

A. closely related to Tyrannosaurus Rex

B. not closely related to Tyrannosaurus Rex

C. not closely related to Giganotosaurus

D. closely related to the large cat family

Để tham gia cân bằng pH nội môi, có bao nhiêu phát biểu sau đây sai?

I.    Để duy trì pH máu có nhờ các hệ đệm prôtêinat, bicacbonat, photphat.

II.  Phổi điều hòa pH nội môi bằng cách thải C O 2

III. Thận điều hòa pH nội môi bằng cách thải H + , tái hấp thụ N a +

IV. Gan điều hòa pH nội môi bằng cách tái hấp thụ N H 3  

A. 1

B. 2

C. 3

D. 4

Đặt A= a²+b²+c²-ab-ac-bc

<=>2A=2a²+2b²+2c²-2ab-2ac-2bc

<=>2A=(a²-2ab+b²)+(a²-2ac+c²)+(b²-2bc+c²)

<=>2A=(a-b)²+(a-c)²+(b-c)²

Ta thấy:(a-b)²>=0 với mọi a,b

(a-c)²>=0 với mọi a, c

(b-c)²>=0 với mọi b, c

=> (a-b)²+(a-c)²+(b-c)²>=0 với mọi a, b, c

=> 2a²+2b²+2c²-2ab-2ac-2bc>=0

=>a²+b²+c²-ab-ac-bc>=0

=>a²+b²+c² >=ab+ac+bc (dpcm)

Trong tự nhiên kali có 3 đồng vị ³⁹K (93,26%), ⁴¹K (x₁%), ⁴⁰K (x₂%), nguyên tử khối trung bình của kali là 39,1347. Giá trị x₁ và x₂ lần lượt là

A. 6,73% và 0,01%.

B. 3,67% và 3,07%.

C. 3,76% và2,98%.

D. 2,89% và 3,85%.

(2k-1)x+3k-5=0

<=>(2k-1)x=5-3k

phương trình vô nghiệm

<=>\(\left\{{}\begin{matrix}2k-1=0\\5-3k#0\end{matrix}\right.\)

<=>\(\left\{{}\begin{matrix}k=\dfrac{1}{2}\\k#\dfrac{5}{3}\end{matrix}\right.\)

Vậy k=\(\dfrac{1}{2}\) thì phương trình vô nghiệm

2

4