Question

phân tích thành nhân tử 

a)5+ căn 3+5 căn 3+3

b) căn x+ căn y+ căn xy +1

c)x- 4 căn x+3

Answer 1

Lời giải:
a.

\(5+\sqrt{3}+5\sqrt{3}+3=(5+5\sqrt{3})+(\sqrt{3}+3)\)

\(=5(1+\sqrt{3})+\sqrt{3}(1+\sqrt{3})=(1+\sqrt{3})(5+\sqrt{3})\)

b.

\(\sqrt{x}+\sqrt{y}+\sqrt{xy}+1=(\sqrt{x}+\sqrt{xy})+(\sqrt{y}+1)\)

\(=\sqrt{x}(1+\sqrt{y})+(\sqrt{y}+1)=(\sqrt{y}+1)(\sqrt{x}+1)\)

c.

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

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

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