Question

Answer 1

Bài 2:

a. $x^3+3xy^2+y^3+3x^2y=250+262$

$\Leftrightarrow (x+y)^3=512=8^3$

$\Leftrightarrow x+y=8$

b. 

$x^3+3xy^2=14$

$y^3+3x^2y=13$

$\Rightarrow x^3+3xy^2-y^3-3x^2y=14-13$

$\Leftrightarrow x^3-3x^2y+3xy^2-y^3=1$

$\Leftrightarrow (x-y)^3=1$

$\Leftrightarrow x-y=1$

Answer 2

Bài 1:

a. $x^2+y^2=(x+y)^2-2xy=8^2-2.15=34$

b. $x^3+y^3=(x+y)^3-3xy(x+y)=8^3-3.15.8=152$

c. $|x^2-y^2|=|x-y||x+y|=8|x-y|=8\sqrt{(x-y)^2}=8\sqrt{(x+y)^2-4xy}$

$=8\sqrt{8^2-4.15}=16$

$\Rightarrow x^2-y^2=16$ hoặc $x^2-y^2=-16$