Question

разложите на множители : а) а +2sqrt а б) sqrt 6 - sqrt 18 в) х^2 -15 г) 4-4sqrt х +х д) 3х + 6 sqrt ху + sqrt х + 2 sqrt у

Answer 1

$a) a+2sqrt{a}=sqrt{a}(sqrt{a}+2)$

 

$b) \ sqrt{6}-sqrt{18}=sqrt{6}-sqrt{3*6}=sqrt{6}(1)-sqrt{3}$

 

c) $x^2 - 15 = x^2 - sqrt{15^2}=x^2 - (sqrt{15})^2=(x-sqrt{15})(x+sqrt{15})$

 

d) $4-4sqrt{x}+x= 2^2-2*2*sqrt{x}+sqrt{x}^2=\ \ =(2-sqrt{x})^2$

 

e)  $3x+6sqrt{xy}+sqrt{x}+2sqrt{y}=\ \ =3x+sqrt{x}+6sqrt{xy}+2sqrt{y}=\ \ =sqrt{x}(3sqrt{x}+1)+2sqrt{y}(3sqrt{x}+1)=\ \ =(3sqrt{x}+1)(sqrt{x}+2sqrt{y})$

Answer 2

а) а+2√а = √а(√а+2)

б) √6-√18 = √6(1-√3)

в) х²-15 = (х-√15)(х+√15)

г) 4-4√х+х = (2-√х)²

д) 3х+6√(ху)+√х+2√у = (3х+√х) + (6√(ху)+2√у) = 

    √х(3√х+1) + 2√у(3√х+1) = (3√х+1)(√х+2√у)