a, \(\sqrt{x^2-6x+9}=2\)

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

\(\Leftrightarrow\left|x-3\right|=2\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=2\\x-3=-2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=1\end{matrix}\right.\)

a: Ta có: \(\sqrt{x^2-6x+9}=2\)

\(\Leftrightarrow\left(x-5\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=1\end{matrix}\right.\)

7: \(\frac{2\sqrt3+3\sqrt2}{\sqrt2+\sqrt3}+\frac12\left(\sqrt2-\sqrt3\right)^2\)

\(=\frac{\sqrt6\left(\sqrt2+\sqrt3\right)}{\sqrt2+\sqrt3}+\frac12\left(5-2\sqrt6\right)\)

\(=\sqrt6+\frac52-\sqrt6=\frac52\)

8: \(\frac{3+2\sqrt3}{\sqrt3}+\frac{2+\sqrt2}{\sqrt2+1}-\left(2+\sqrt3\right)\)

\(=2+\sqrt3+\frac{\sqrt2\left(\sqrt2+1\right)}{\sqrt2+1}-2-\sqrt3\)

\(=\sqrt2\)

9: \(\frac{1}{\sqrt5-2}+\frac{1}{\sqrt5+2}\)

\(=\frac{\sqrt5+2+\sqrt5-2}{\left(\sqrt5-2\right)\left(\sqrt5+2\right)}=\frac{2\sqrt5}{5-4}=2\sqrt5\)

10: \(\frac{2}{4-3\sqrt2}-\frac{2}{4+3\sqrt2}\)

\(=\frac{2\left(4+3\sqrt2\right)-2\left(4-3\sqrt2\right)}{\left(4+3\sqrt2\right)\left(4-3\sqrt2\right)}\)

\(=\frac{8+6\sqrt2-8+6\sqrt2}{16-18}=\frac{12\sqrt2}{-2}=-6\sqrt2\)

11: \(\frac{2+\sqrt2}{1+\sqrt2}-\frac{2-\sqrt2}{1-\sqrt2}\)

\(=\frac{\sqrt2\left(1+\sqrt2\right)}{1+\sqrt2}+\frac{\sqrt2\left(\sqrt2-1\right)}{\sqrt2-1}\)

\(=\sqrt2+\sqrt2=2\sqrt2\)

12: \(\left(\sqrt2-\sqrt6\right)\cdot\sqrt{2+\sqrt3}\)

\(=\left(1-\sqrt3\right)\cdot\sqrt{4+2\sqrt3}\)

\(=\left(1-\sqrt3\right)\left(\sqrt3+1\right)=\left(1-\sqrt3\right)\left(1+\sqrt3\right)\)

=1-3

=-2

cái avt :V

avt ghê v

a: \(M=2\left(x+5\right)^2+5\left(x-2\right)^2-7\left(x+3\right)\left(x-3\right)\)

\(=2\left(x^2+10x+25\right)+5\left(x^2-4x+4\right)-7\left(x^2-9\right)\)

\(=2x^2+20x+50+5x^2-20x+20-7x^2+63\)

\(=113\)

b: \(H=\left(2x-3y\right)^2-\left(3y-2\right)\left(3y+2\right)-\left(1-2x\right)^2+4x\left(3y-1\right)\)

\(=4x^2-12xy+9y^2+12xy-4x-\left(9y^2-4\right)-\left(4x^2-4x+1\right)\)

\(=4x^2+9y^2-4x-9y^2+4-4x^2+4x-1\)

=3

c: \(N=\left(2x+3y\right)^2+\left(3x-2y\right)^2-13\left(x+y\right)\left(x-y\right)-26\left(y+1\right)\left(y-1\right)\)

\(=4x^2+12xy+9y^2+9x^2-12xy+4y^2-13\left(x^2-y^2\right)-26\left(y^2-1\right)\)

\(=13x^2+13y^2-13x^2+13y^2-26y^2+26\)

=26

d: \(K=\left(x^2y-3\right)^2-\left(2x-y\right)^3+xy^2\left(6-x^3\right)+8x^3-6x^2y-y^3\)

\(=x^4y^2-6x^2y+9+6xy^2-x^4y^2+8x^3-6x^2y-y^3-\left(2x-y\right)^3\)

\(=-12x^2y+9-y^3+6xy^2+8x^3-\left(8x^3-12x^2y+6xy^2-y^3\right)\)

\(=\left(8x^3-12x^2y+6xy^2-y^3\right)-\left(8x^3-12x^2y+6xy^2-y^3\right)+9\)

=9

e: \(P=\left(4x+3\right)\left(16x^2-12x+9\right)-\left(-23+64x^3\right)\)

\(=\left(4x\right)^3+3^3+23-64x^3\)

\(=64x^3+27+23-64x^3\)

=50

h: \(Q=\left(x+5y\right)\left(x^2-5xy+25y^2\right)+\left(x-5y\right)\left(x^2+5xy+25y^2\right)-\dfrac{1}{2}\left(4x^3-7\right)\)

\(=x^3+125y^3+x^3-125y^3-2x^3+\dfrac{7}{2}\)

=7/2

cảm on ạa

IV.

21. a -> an

22. polluted -> pollution

23. noisy -> noisier

24. Lucky -> Luckily

25. learning -> to learn

V.

26. visit her friend because she doesn't have time.

27. how much I thought it would cost.

28. gone aboard before.

29. been used for three months.

30. is considered to be one of the best.

IV:

21. an hour

22.

23. noisier

24. Luckily

25. to learn

V:

26.

She won't visit her friends because she hasn't time.

27.

He asked me how much I thought it would cost.

28

He hasn't gone abroad before.

29.

That computer has been used for 3 months.

30.

His speech was considered one of the best

ảnh mang tính chất minh họa:?