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a: \(\Leftrightarrow\dfrac{x^4+2x^2+1-x^2}{x^2}=\dfrac{x^2+x+1}{x}\)

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

\(\Leftrightarrow\dfrac{x^2-x+1}{x^2}=\dfrac{1}{x}\)

=>x^2=x(x^2-x+1)

=>x(x-x^2+x-1)=0

=>x(-x^2+2x-1)=0

=>x=0(loại) hoặc x=1(nhận)

b: =>3(x+3)^2*(x+2)^2/(x^2-4)^2+68*(x-3)^2*(x-2)^2/(x^2-4)^2-46(x^2-9)(x^2-4)=6(x^2-4)^2

=>3(x^2+5x+6)^2+68(x^2-5x+6)^2-46(x^4-13x^2+36)=6(x^4-8x^2+16)

=>\(x\simeq28,4\)

\(\Leftrightarrow\dfrac{\left(x^2-3x+2\right)^2+\left(x^2+3x+2\right)^2}{\left(x^2-1\right)^2}-\dfrac{11\left(x^4-5x^2+4\right)}{\left(x^2-1\right)^2}=0\)

\(\Leftrightarrow\left(x^2-3x+2\right)^2+\left(x^2+3x+2\right)^2-11\left(x^4-5x^2+4\right)=0\)
\(\Leftrightarrow\left(x^2+2\right)^2-6x\left(x^2+2\right)+9x^2+\left(x^2+2\right)^2+6x\left(x^2+2\right)+9x^2-11\left(x^4-5x^2+4\right)=0\)

\(\Leftrightarrow2\left(x^2+2\right)^2+18x^2-11x^4+55x^2-44=0\)

\(\Leftrightarrow2\left(x^4+4x^2+4\right)-11x^4+73x^2-44=0\)

=>\(-9x^4+81x^2-36=0\)

=>9x^4-81x^2+36=0

=>x^4-9x^2+4=0

=>\(x^2=\dfrac{9\pm\sqrt{65}}{2}\)

=>\(x=\pm\sqrt{\dfrac{9\pm\sqrt{65}}{2}}\)

a: \(=\dfrac{1}{x-y}\cdot x^2\cdot\left(x-y\right)=x^2\)

b: \(=\sqrt{27\cdot48}\cdot\left|a-2\right|=36\left(a-2\right)\)

c: \(=\left(\sqrt{2012}+\sqrt{2011}\right)^2\)

d: \(=\dfrac{8}{7}\cdot\dfrac{-x}{y+1}\)

e: \(=\dfrac{11}{12}\cdot\dfrac{x}{-y-2}=\dfrac{-11x}{12\left(y+2\right)}\)

1 tháng 5 2022

1, vt : \(\left(1-\dfrac{5+\sqrt{2}}{\sqrt{2}+1}\right).\sqrt{3+2\sqrt{2}}\)

=\(\dfrac{\sqrt{2}+1-5-\sqrt{2}}{\sqrt{2}+1}.\sqrt{\left(\sqrt{2}\right)^2+2\sqrt{2}+1}\)

=\(\dfrac{-4}{\sqrt{2}+1}.\sqrt{\left(\sqrt{2}+1\right)^2}\)

=\(\dfrac{-4\left(\sqrt{2}+1\right)}{\sqrt{2}+1}\)

=-4

2, A=\(\left(\dfrac{\sqrt{x}}{x+\sqrt{x}}-\dfrac{1}{\sqrt{x}-1}\right)\div\dfrac{2}{x+\sqrt{x}-2}\)

=\(\left(\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)-x-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right).\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}{2}\)

=\(\left(\dfrac{x-\sqrt{x}-x-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right).\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{2}\)

=\(\dfrac{-2\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}.\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}{2}\)

=\(\dfrac{-\sqrt{x}-2}{\sqrt{x}+1}\)

a: ĐKXĐ: x>1; x<>2

b: \(P=\left(\dfrac{\sqrt{x}+\sqrt{x-1}}{x-x+1}-\sqrt{x-1}-\sqrt{2}\right)\cdot\dfrac{2\sqrt{x}-\sqrt{x}-\sqrt{2}}{\sqrt{x}\left(\sqrt{2}-\sqrt{x}\right)}\)

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

c: Khi x=3+2căn 2 thì

P=(-căn 2-1+căn 2)/(căn 2+1)=căn 2-1

2 tháng 9 2017

câu b đk x>= -1/4

\(x+\sqrt{x+\dfrac{1}{2}+\sqrt{x+\dfrac{1}{4}}}=2\)

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

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

\(x+\dfrac{1}{4}=\left(\sqrt{2}-\dfrac{1}{2}\right)^2\)

\(x=\left(\sqrt{2}-\dfrac{1}{2}\right)^2-\dfrac{1}{4}\)

\(x=\left(\sqrt{2}-\dfrac{1}{2}-\dfrac{1}{2}\right)\left(\sqrt{2}-\dfrac{1}{2}+\dfrac{1}{2}\right)\)

\(x=\sqrt{2}\left(\sqrt{2}-1\right)=2-\sqrt{2}\)

3 tháng 9 2017

bạn ghi cai gì vậy hả. Mình chẳng hiểu gì hết ý

Rút gọn: \(M=1-\left[\dfrac{2x-1+\sqrt{x}}{1-x}+\dfrac{2x\sqrt{x}+x-\sqrt{x}}{1+x\sqrt{x}}\right]\cdot\left[\dfrac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}\right]\) Giải:: ĐK: x khác +- 1...
Đọc tiếp

Rút gọn:

\(M=1-\left[\dfrac{2x-1+\sqrt{x}}{1-x}+\dfrac{2x\sqrt{x}+x-\sqrt{x}}{1+x\sqrt{x}}\right]\cdot\left[\dfrac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}\right]\)

Giải::

ĐK: x khác +- 1

\(M=1-\left[\dfrac{\left(\sqrt{x}-\dfrac{1}{2}\right)\left(\sqrt{x}+1\right)}{\left(1+\sqrt{x}\right)\left(1-\sqrt{x}\right)}+\dfrac{\sqrt{x}\left(\sqrt{x}-\dfrac{1}{2}\right)\left(\sqrt{x}+1\right)}{\left(1+\sqrt{x}\right)\left(1-\sqrt{x}+x\right)}\right]\cdot\left[\dfrac{-\sqrt{x}\left(1-\sqrt{x}\right)^2}{2\left(\sqrt{x}-\dfrac{1}{2}\right)}\right]\)

\(=1-\left[\dfrac{\left(\sqrt{x}-\dfrac{1}{2}\right)}{\left(1-\sqrt{x}\right)}\cdot\dfrac{-\sqrt{x}\left(1-\sqrt{x}\right)^2}{2\left(\sqrt{x}-\dfrac{1}{2}\right)}+\dfrac{\sqrt{x}\left(\sqrt{x}-\dfrac{1}{2}\right)}{1-\sqrt{x}+x}\cdot\dfrac{-\sqrt{x}\left(1-\sqrt{x}\right)^2}{2\left(\sqrt{x}-\dfrac{1}{2}\right)}\right]\)

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

rồi làm sao nữa ak?? Tớ có quy đồng lên, tính sơ sơ rồi nhưng thấy kq không gọn.

Câu b là : tìm các số nguyên x để M cũng là số nguyên . Nên tớ nghĩ kq sẽ gọn.

NHỜ MẤY CAO NHÂN RA TAY GIÚP VỚI NHAK ^^!

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