АЛГЕБРА 8 КЛАС
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2X - Y = 2 ; Y = 2X - 2 
2X^2 - X * ( 2X - 2 ) = 6 
2X^2 - 2X^2 + 2X = 6 
2X = 6 
X = 3 
Y = 6 - 2 = 4 
ОТВЕТ ( 3 ; 4 ) 

( X + 2 )*( Y + 1 ) = 12 
X + 2Y = 6 ; X = 6 - 2Y 
( 6 - 2Y + 2 )*( Y + 1 ) = 12 
( 8 - 2Y )*( Y + 1 ) = 12 
8Y + 8 - 2Y^2 - 2Y = 12 
- 2Y^2 + 6Y - 4 = 0 
- 2 * ( Y^2 - 3Y + 2 ) = 0 
D = 9 - 8 = 1 ; √ D = 1 
Y1 = ( 3 + 1 ) : 2 = 2 
Y2 = ( 3 - 1 ) : 2 = 1 
X1 = 6 - 4 = 2 
X2 = 6 - 2 = 4 
ОТВЕТ ( 2 ; 2 ) ; ( 4 ; 1 ) 

X^2 + Y^2 = 10 
XY = - 3 
X = ( - 3 / Y ) ; X^2 = 9 / Y^2 
( 9 / Y^2 ) + Y^2 = 10 
( 9 + Y^4 ) / Y^2 = 10 ( Y ≠ 0 ) 
9 + Y^4 = 10Y^2 
Y^4 - 10Y^2 + 9 = 0 
Y^2 = A ; A > 0 
A^2 - 10A + 9 = 0 
D = 100 - 36 = 64 ; √ D = 8 
A1 = ( 10 + 8 ) : 2 = 9 
A2 = ( 10 - 8 ) : 2 = 1 
Y^2 = 9 ===> Y (1 /2 ) = ( + / - ) 3 
Y^2 = 1 ===> Y ( 3/4 ) = ( +/ - ) 1 
X^2 = 9 / Y^2 
X^2 = 9 / 9 = 1 ===> X ( 1/2 ) = ( + / - ) 1 
X^2 = 9 / 1 = 9 ===> X ( 3/4 ) = ( + / - ) 3 
ОТВЕТ ( 1 ;  3 );  ( - 1 ;  - 3  );   ( 3  ;  1 ) ;  ( - 3 ; - 1 ) 

Объяснение:

А) 5x^3 - 3x^2 - 3x + 5 = 0

5x^3 + 5 - 3x^2 - 3x = 0

5(x^3 + 1) - 3x(x + 1) = 0

5(x + 1)(x^2 - x + 1) - 3x(x + 1) = 0

(x + 1)(5x^2 - 5x + 5 - 3x) = 0

(x + 1)(5x^2 - 8x + 5) = 0

x + 1 = 0 => x = -1

5x^2 - 8x + 5 = 0

D = 8^2 - 4 * 5 * 5 = 64 - 100 = -36

∅

ответ: x = -1

Б) (x + 1/x)^2 - 5(x + 1/x) + 6 = 0

t = x + 1/x

t^2 - 5t + 6 = 0

D = 5^2 - 4 * 1 * 6 = 25 - 24 = 1

t1 = (5 + 1) / 2 = 6/2 = 3

t2 = (5 - 1) / 2 = 4/2 = 2

x + 1/x = 3

x^2 - 3x + 1 = 0

D = 3^2 - 4 * 1 * 1 = 9 - 4 = 5

x1 = (3 - √5) / 2

x2 = (3 + √5) / 2

x + 1/x = 2

x^2 - 2x + 1 = 0

D = 2^2 - 4 * 1 * 1 = 4 - 4 = 0

x = 2 / 2 = 1

ответ: x1 = (3 - √5) / 2 ; x2 = 1 ; x3 = (3 + √5) / 2.