Question

Aflați numerele naturale x si y , știind ca :

a)(2x+3)×(2x+4)=56
b)(2x+1)×(2x+2)×(2x+3)=720
c)(x-1)×(y+2)=13

Answer 1

a) (2x)² + 2x•4 + 3•2x + 12 = 56
2²x²+8x+6x+12 = 56
4x² + 14x - 44 = 0
2²x²+8x+6x+12 - 56 = 56-56
2 = 0 sau x-2 = 0
sau 2x + 11 = 0
x = 2; x = -11/2.

b) (2x+3) ((2x)² + 2x•2+1•2x+2) = 720
(2x+3) (2²x²+4x+2x+2) = 720
(2x+1) (2x+2) (2x+3) = 720
(2x+3) (4x²+6x+2) = 720
2x•4x²+2x•6x+2x•2+3•4x²+3•6x+6 = 720
8x³+12x²+12x²+4x+18x+6 = 720
(2x-7) (4x²+20x+102) = 0
x = 0 sau 2x - 7 = 0.

c) x - 1 = 13 / y+2
(x-1) (y+2) / (y+2) = 13 / (y+2)
x = 13 + (y+2) / y+2
x - 1 + 1 = 13 / y+2 +1
x = y+2+13 / y+2
x = y+15 / y+2

y+2 = 13 / x-1
(x-1) (y+2) / (x-1) = 13 / (x-1)
y = 13+ -2x + 2 / x-1
y+2-2 = 13 / x-1 -2
y = -2x + 15 / x-1.