a)\(\Rightarrow P=\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)+2\sqrt{x}\left(\sqrt{x}-2\right)-5\sqrt{x}-2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)

\(=\dfrac{x+3\sqrt{x}+2+2x-4\sqrt{x}-5\sqrt{x}-2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)

\(=\dfrac{3x-6\sqrt{x}}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}=\dfrac{3\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{3\sqrt{x}}{\sqrt{x}+2}\)

b) Ta có P=2

\(\dfrac{\Leftrightarrow3\sqrt{x}}{\sqrt{x}+2}=2\Leftrightarrow3\sqrt{x}=2\sqrt{x}+4\)

\(\Leftrightarrow\sqrt{x}=4\Leftrightarrow x=16\left(n\right)\)

Vậy x=16 thì P=2

\(\Leftrightarrow16x^4+5-6=6\sqrt[3]{4x^3+x}-6\)

\(\Leftrightarrow16x^4-1=6\left(\sqrt[3]{4x^3+x}-1\right)\)

\(\Leftrightarrow\left(4x^2-1\right)\left(4x^2+1\right)=6\left[\dfrac{4x^3+x-1}{\left(\sqrt[3]{4x^3+x}\right)^2+\sqrt[3]{4x^3+x}+1}\right]\)

\(\Leftrightarrow\left(2x+1\right)\left(2x-1\right)\left(4x^2+1\right)-6\left(\dfrac{\left(2x-1\right)\left(2x^2+x+1\right)}{\left(\sqrt[3]{4x^3+x}\right)^2+\sqrt[3]{4x^3+x}+1}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\\left(2x+1\right)\left(4x^2+1\right)=\dfrac{6\left(2x^2+x+1\right)}{\left(\sqrt[3]{4x^3+x}\right)^2+\sqrt[3]{4x^3+x}+1}\left(l\right)\end{matrix}\right.\)

Vậy S=\(\left\{\dfrac{1}{2}\right\}\)

đề có sai không bn

Ta có\(\left(x+\sqrt{x^2+2012}\right)\left(y+\sqrt{y^2+2012}\right)=2012\) đk \(\left\{{}\begin{matrix}x^2+2012\ge0\\y^2+2012\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left(x-\sqrt{x^2+2012}\right)\left(x+\sqrt{x^2+2012}\right)\left(y+\sqrt{y^2+2012}\right)=2012\left(x-\sqrt{x^2+2012}\right)\)

\(\Leftrightarrow\left(x^2-x^2-2012\right)\left(y+\sqrt{y^2+2012}\right)=2012\left(x-\sqrt{x^2+2012}\right)\)

\(\Leftrightarrow-2012\left(y+\sqrt{y^2+2012}\right)=2012\left(x-\sqrt{x^2+2012}\right)\)

\(\Leftrightarrow-y-\sqrt{y^2+2012}=x-\sqrt{x^2+2012}\)

\(\Leftrightarrow x+y-\left(\sqrt{x^2+2012}-\sqrt{y^2+2012}\right)=0\)

\(\Leftrightarrow x+y-\dfrac{\left(x-y\right)\left(x+y\right)}{\sqrt{x^2+2012}+\sqrt{y^2+2012}}=0\)

\(\Leftrightarrow\left(x+y\right)\left(1-\dfrac{x-y}{\sqrt{x^2+2012}+\sqrt{y^2+2012}}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+y=0\\1=\dfrac{x-y}{\sqrt{x^2+2012}+\sqrt{y^2+2012}}\left(loại\right)\end{matrix}\right.\)

\(\Rightarrow E=0\)

B

CHo 3 số nguyên a,b,c thỏa mãn \(\left(a^3+b^3\right)\left(b^3+c^3\right)\left(c^3+a^3\right)\)chia hết cho 5 Chứng minh rằng (a+b)(b+c)(c+a) chia hết cho 5

Tìm  tất cả số nguyên tố p và các số nguyên dương x,y thỏa mãn \(199^x-2^x=p^y\)

CHo 3 số nguyên a,b,c thỏa mãn \(\left(a^3+b^3\right)\left(b^3+c^3\right)\left(c^3+a^3\right)\)chia hết cho 5 Chứng minh rằng (a+b)(b+c)(c+a) chia hết cho 5

CHo 2 số nguyên a,b(a\(\ge\)b) và số nguyên dương c thỏa mãn a(a+1)+b(b-1)=c(c+1)

tính giá trị biểu thức A =3c-5b