a) x²- 7= \(\left(x-\sqrt{7}\right)\left(x+\sqrt{7}\right)\)

b) \(x^2-2\sqrt{2}x+2=\left(x-\sqrt{2}\right)^2\)

c) \(x^2+2\sqrt{13}x+13=\left(x+\sqrt{13}\right)^2\)

a, x²-7=\(\left(x-\sqrt{7}\right)\left(x+\sqrt{7}\right)\)

b, x²-3=\(\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)\)

Học tốt!!!!!!!!!!

a/ \(x^2-7\)

\(=\left(x-\sqrt{7}\right)\left(x+\sqrt{7}\right)\)

b/ \(x^2-3\)

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

c/ \(x^2-2\sqrt{13}x+13\)

\(=\left(x-\sqrt{13}\right)^2\)

Mấy bài này áp dụng HĐT nhé bạn :3

d: \(=-\left(x+\sqrt{x}-12\right)=-\left(\sqrt{x}+4\right)\left(\sqrt{x}-3\right)\)

a: =(căn a-3)^2-b^2

=(căn a-3-b)(căn a-3+b)

b: \(x-9=\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)\)

c: \(x-7\sqrt{x}+12=x-3\sqrt{x}-4\sqrt{x}+12=\left(\sqrt{x}-3\right)\left(\sqrt{x}-4\right)\)

d: x*căn x-64

=(căn x)^3-4^3

=(căn x-4)(x+4căn x+16)

\(a-6\sqrt{a}+9-b^2\\ =\left(\sqrt{a}+3\right)^2-b^2\\ =\left(\sqrt{a}+3-b\right)\left(\sqrt{a}+3+b\right)\)

\(x-9=\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)\)

\(x-7\sqrt{x}+12\\ =x-4\sqrt{x}-3\sqrt{x}+12\\ =\sqrt{x}\left(\sqrt{x}-4\right)-3\left(\sqrt{x}-4\right)\\ =\left(\sqrt{x}-4\right)\left(\sqrt{x}-3\right)\)

\(x\sqrt{x}+64\\ =\sqrt{x^3}+4^3\\ =\left(\sqrt{x}\right)^3+4^3\\ =\left(\sqrt{x}+4\right)\left(x-4\sqrt{x}+16\right)\)

Lời giải:
a.

$7-3a=(\sqrt{7}-\sqrt{3a})(\sqrt{7}+\sqrt{3a})$

b. 

$14x^2-11=(\sqrt{14}x-\sqrt{11})(\sqrt{14}x+\sqrt{11})$

c.

$3x-6\sqrt{x}-6=3(x-2\sqrt{x}-2)$
$=3[(\sqrt{x}-1)^2-3]$

$=3(\sqrt{x}-1-\sqrt{3})(\sqrt{x}-1+\sqrt{3})$

d.

$x\sqrt{x}-3\sqrt{x}-2=x\sqrt{x}-2x+2x-4\sqrt{x}+\sqrt{x}-2$
$=x(\sqrt{x}-2)+2\sqrt{x}(\sqrt{x}-2)+(\sqrt{x}-2)$

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

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

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

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

b) \(x-2\sqrt{x-6}-5-y^2=\left(x-6\right)-2\sqrt{x-6}+1-y^2\)

\(=\left(\sqrt{x-6}-1\right)^2-y^2=\left(\sqrt{x-6}-1+y\right)\left(\sqrt{x-6}-1-y\right)\)

c) \(x-2\sqrt{x-8}-7-a^2=\left(x-8\right)-2\sqrt{x-8}+1-a^2\)

\(=\left(\sqrt{x-8}-1\right)^2-a^2=\left(\sqrt{x-8}+a-1\right)\left(\sqrt{x-8}-a-1\right)\)

a) \(\left(\sqrt{x-1}-3\right)\left(\sqrt{x-1}+1\right)\)

b) \(\left(\sqrt{x-6}-1-y\right)\left(\sqrt{x-6}-1+y\right)\)

c) \(\left(\sqrt{x-8}-1-a\right)\left(\sqrt{x-8}-1+a\right)\)

a/ \(\left(\sqrt{x-1}-3\right)\left(\sqrt{x-1}+2\right)\)

b/ \(\left(\sqrt{x-6}-1-y\right)\left(\sqrt{x-6}-1+y\right)\)

c/\(\left(\sqrt{x-8}-1-a\right)\left(\sqrt{x-8}-1+a\right)\)

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

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

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

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