đây là toàn lp 3 hả bn

đây ko phải toán lớp 3

a, \(\frac{\sqrt{2}\left(1-\sqrt{3}\right)}{1-\sqrt{3}}\)-\(\frac{3\left(1+\sqrt{3}\right)}{1+\sqrt{3}}\)

=\(\sqrt{2}-3\)

b,X=\(\sqrt{2019}+\sqrt{2018}\)

(Khử mẫu,nhân tử&mẫu vs\(\sqrt{2019}+\sqrt{2018}\))

Y=\(\sqrt{2018}+\sqrt{2017}\)

(Khử mẫu,nhân tử&mẫu vs\(\sqrt{2018}+\sqrt{2017}\))

So sánh:X & Y<=>X-\(\sqrt{2018}\)&Y-\(\sqrt{2018}\)(Trừ hai vế cho \(\sqrt{2018}\)) <=>\(\sqrt{2019}\)&\(\sqrt{2017}\)

Có:2019>2017

=>\(\sqrt{2019}>\sqrt{2017}\)

=>X>Y

Câu b, mk ko bt có lm đúng ko?

từ a+b=3 => b=3-a

mặt khác: \(a^3-b^2=-3\)

=>\(a^3-\left(3-a\right)^2+3=0\)

\(\Rightarrow a^3-9+6a-a^2+3=0\)

\(\Rightarrow a^3-a^2+6a-6=0\)

\(\Rightarrow a^2\left(a-1\right)+6\left(a-1\right)=0\)

\(\Rightarrow\left(a^2+6\right)\left(a-1\right)=0\)

\(\Rightarrow\hept{\begin{cases}a^2+6=0\\a-1=0\end{cases}\Rightarrow\hept{\begin{cases}a^2=-6\\a=1\end{cases}}}\)

=>a=1 vì \(a^2\ge0\)

=>\(\sqrt[3]{x-2}=1\)

\(\Rightarrow x-2=1\Rightarrow x=3\)

Vậy x=3

b) ta có: Đặt :\(\sqrt[3]{x-2}=a;\)    Đk: \(x\ge-1\)

                \(\sqrt{x+1}=b;b\ge0\)

ta có:\(\hept{\begin{cases}a+b=3\\a^3-b^2=-3\end{cases}}\)

đến đây dùng pp thế là đc rồi nhé!

a/ ĐKXĐ: \(x\ge2\)

\(\Leftrightarrow2\sqrt{\left(x-2\right)\left(x+2\right)}-6\sqrt{x-2}+\sqrt{x+2}-3=0\)

\(\Leftrightarrow2\sqrt{x-2}\left(\sqrt{x+2}-3\right)+\sqrt{x+2}-3=0\)

\(\Leftrightarrow\left(2\sqrt{x-2}+1\right)\left(\sqrt{x+2}-3\right)=0\)

\(\Leftrightarrow\sqrt{x+2}-3=0\Rightarrow x=11\)

b/ ĐKXĐ: ....

Đặt \(\left\{{}\begin{matrix}\sqrt{x-2016}=a>0\\\sqrt{y-2017}=b>0\\\sqrt{z-2018}=a>0\end{matrix}\right.\)

\(\frac{a-1}{a^2}+\frac{b-1}{b^2}+\frac{c-1}{c^2}=\frac{3}{4}\)

\(\Leftrightarrow\frac{1}{4}-\frac{a-1}{a^2}+\frac{1}{4}-\frac{b-1}{b^2}+\frac{1}{4}-\frac{c-1}{c^2}=0\)

\(\Leftrightarrow\frac{\left(a-2\right)^2}{a^2}+\frac{\left(b-2\right)^2}{b^2}+\frac{\left(c-2\right)^2}{c^2}=0\)

\(\Leftrightarrow a=b=c=2\Rightarrow\left\{{}\begin{matrix}x=2020\\y=2021\\z=2022\end{matrix}\right.\)

a/ ĐK: \(x\ge0\)

\(\Leftrightarrow\sqrt{3+x}=x^2-3\)

Đặt \(\sqrt{3+x}=a>0\Rightarrow3=a^2-x\) pt trở thành:

\(a=x^2-\left(a^2-x\right)\)

\(\Leftrightarrow x^2-a^2+x-a=0\)

\(\Leftrightarrow\left(x-a\right)\left(x+a+1\right)=0\)

\(\Leftrightarrow x=a\) (do \(x\ge0;a>0\))

\(\Leftrightarrow\sqrt{3+x}=x\Leftrightarrow x^2-x-3=0\)

d/ ĐKXĐ: ...

\(\sqrt{6x^2+1}=\sqrt{2x-3}+x^2\)

\(\Leftrightarrow\sqrt{2x-3}-1+x^2+1-\sqrt{6x^2+1}\)

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

\(\Leftrightarrow\frac{2\left(x-2\right)}{\sqrt{2x-3}+1}+\frac{x^2\left(x+2\right)\left(x-2\right)}{\left(x^2+1\right)^2+\sqrt{6x^2+1}}=0\)

\(\Leftrightarrow\left(x-2\right)\left(\frac{2}{\sqrt{2x-3}+1}+\frac{x^2\left(x+2\right)}{\left(x^2+1\right)^2+\sqrt{6x^2+1}}\right)=0\)

\(\Leftrightarrow x=2\) (phần trong ngoặc luôn dương với mọi \(x\ge\frac{3}{2}\))

Đặt \(2018=a\)

\(\Rightarrow\sqrt{a-1+\sqrt{x-1}}=a-x\)

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

\(\Leftrightarrow\sqrt{x-1}=x^2-2ax+a^2-a+1\)

\(\Leftrightarrow x-1=\left(x^2-2ax+a^2-a+1\right)^2\)

\(\Leftrightarrow\left[\left(x-a\right)^2-x+1\right]\left[\left(x-a\right)^2+x-2a+2\right]=0\)

Bài 1:

\(x^4+2x^3+10x-25=0\)

\(\Leftrightarrow x^4+2x^3-5x^2+5x^2+10x-25=0\)

\(\Leftrightarrow x^2\left(x^2+2x-5\right)+5\left(x^2+2x-5\right)=0\)

\(\Leftrightarrow\left(x^2+5\right)\left(x^2+2x-5\right)=0\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x^2+5=0\\x^2+2x-5=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x^2+5>0\forall x\rightarrow Vn\\\Delta_{x^2+2x-5}=2^2-\left[-4\left(1.5\right)\right]=24\end{array}\right.\)

\(\Leftrightarrow x_{1,2}=\frac{-2\pm\sqrt{24}}{2}\)

Bài 2:

Đặt \(\begin{cases}\sqrt{x-1}=a\left(a\ge1\right)\\\sqrt{y}=b\left(b\ge0\right)\end{cases}\)(*) hệ đầu thành:

\(\begin{cases}3a+2b=13\left(1\right)\\2a-b=4\left(2\right)\end{cases}\).Từ \(\left(2\right)\Rightarrow b=2a-4\) thay vào (1) ta có:

\(\left(1\right)\Rightarrow3a+2\left(2a-4\right)=13\)

\(\Rightarrow3a+4a-8=13\Rightarrow7a=21\Rightarrow a=3\) (thỏa mãn)

\(a=3\Rightarrow b=2a-4=2\cdot3-4=2\) (thỏa mãn)

Thay \(\begin{cases}a=3\\b=2\end{cases}\) vào (*) ta có:

(*)\(\Leftrightarrow\begin{cases}\sqrt{x-1}=3\\\sqrt{y}=2\end{cases}\)\(\Leftrightarrow\begin{cases}x-1=9\\y=4\end{cases}\)\(\Leftrightarrow\begin{cases}x=10\\y=4\end{cases}\)