6^2.(6+3)+3^3/-13=36.3^2+3^3/-13=3^2(36+3)/-13=9.39/-13=-27

2^10.3^8-2.3^9.2^9 / 2^10.3^8+3^8.2^8.2^2.5

=2^10.3^8(1-3) / 2^10.3^8(1+5)

=-2/6=-1/3

\(\frac{6^3+3.6^2+3^3}{13}=\frac{6^3+108+3^3}{13}.\)

\(=\frac{216+108+27}{13}=\frac{324+27}{13}\)

\(=\frac{351}{13}=27\)

\(\frac{6^3+3\cdot6^2+3^3}{13}=\frac{2^3\cdot3^3+3\cdot3^2\cdot2^2+3^3}{13}=\frac{3^3\left(2^3+2^2+1\right)}{13}=\frac{27\cdot13}{13}=27\)

\(=\frac{\left(3.2\right)^3+3.\left(3.2\right)^2+3^3}{-13}=\frac{3^3.2^3+3^3.3.2^2+3^3}{-13}=\frac{3^3\left(2^3+3.2^2+1\right)}{-13}=\frac{27.21}{-13}=\frac{-567}{13}\)

Ta có :

\(\left(x+y\right)^2=3^2\)

\(x^2+y^2+2xy=9\)

Mà : \(x^2+y^2=13\)

\(\Rightarrow2xy=9-13==-4\)

\(\Rightarrow xy=-2\)

Có : \(x^3+y^3=\left(x+y\right)\left(x^2+y^2-xy\right)\)

                      \(=3\left[13-\left(-2\right)\right]\)

                      \(=3.15=45\)

a) -( x-y)² - (x-1)² -2 

GTLN = -2

a:

A = 2x - 2xy - 2x^2 - y^2

A = -(x^2 + 2xy + y^2) - (x^2 - 2x + 1) + 1

A = -(x + y)^2 - (x - 1)^2 + 1

Vì (x + y)^2 ≥ 0 ∀ x; y; (x - 1)^2 ≥ 0 ∀ x suy ra:

-(x + y)^2 ≤ 0 và (x - 1)^2 ≤ 0 ∀ x; y

A = -(x + y)^2 - (x - 1)^2 + 1 ≤ 1 ∀ x; y

Dấu bằng xảy ra khi x - 1 = 0 và x + y = 0

x - 1 = 0

x = 1

x + y = 0

y = - x

y = - 1

Vậy Amin = 1 khi x = 1; y = - 1

A = (x^2 + 2x + y^2