Respuestas
SOLUCIÓN :
1 ) 2x *( 2x+2) = 7568
4x² + 4x - 7568 =0 ÷4
x²+ x - 1892 =0
x = -1-+87 /2
x = 43
2*x = 2*43 = 86
2x+2 = 2*43 +2 = 88
2) x + y = 215
x* y = 10500
x = 215 - y
( 215-y )* y = 10500
y²-215y +10500 =0
y = 215-+ 65 /2
y = 140 y = 75
x = 75 x = 140 .
Los números son : 140 y 75 .
3) x - y = 12
x* y = 2268
x = 12+ y
( 12+y )*y = 2268
y² + 12y -2268 =0
y = -12-+96/2 = 42
x= 12+ 42 = 54
4) x² -y² = 39
x²+ y² = 89
2x² = 128
x² = 128/2 = 64
x = √64 = 8
y= √89 -64 = 5
x = 8 y = 5
5) 2x , 2x+ 2 , 2x +4 pares consecutivos
( 2x +4 )² = (2x +2)² + ( 2x)²
4x²+ 16x + 16 = 4x²+ 8x + 4 + 4x²
4x²- 8x -12=0 ÷4
x²- 2x - 3 =0
( x - 3) ( x + 1)=0
x = 3 x = -1
2*x = 2*3 = 6
2*x + 2 = 2*3 + 2 = 8
2*x+4 = 2*3+4 = 10
6) x - y = 20 m
A = x*y/2 = 224 m²
x* y = 224*2 = 448
x = y + 20
( y + 20 )* y = 448
y² + 20y - 448 =0
y = 13.405 m
x = 13.405 m + 20 m = 33.405 m
7 ) A cuadrado = 100 m²
L+ 4m → A + 98 m²
L=?
A=L² → L= √A = √100m² = 10m .
A = ( 14 )² = 196 m²
196 m²- 100m² = 96 m²
8) c = 45 m
a/b= 3/4 → 4a = 3b → a = 3b/4