Question

Dacă x-2y =6 și x•2 - 4y•2 =24, atunci valoarea numărului a=x+2y+(x+2y)•2+(x+2y)•3+(x+2y)•4 este = ?

Answer 1

x-2y=6
x=2y+6

x•2-4y•2=24
(2y+6)•2-4y•2=24
(2y+6)•2-8y=24
4y+12-8y=24
12-4y=24
-4y=12
y=-3

a=x+2y+(x+2y)•2+(x+2y)•3+(x+2y)•4

a=(2y+6)+2y+((2y+6)+2y)•2+((2y+6)+2y)•3+((2y+6)+2y)•4

a=(2(-3)+6)+2(-3)+((2(-3)+6)+2(-3))•2+((2(-3)+6)+2(-3))•3+((2(-3)+6)+2(-3))•4

a=(-6+6)-6+((-6+6)-6)•2+((-6+6)-6)•3+((-6+6)-6)•4

a=0-6-6•2-6•3-6•4

a=-6-12-18-24
a=-60


OR

x-2y=6
x=2y+6


`x^(2) -4 y^(2) =24`

`(2y+6) ^(2) -4y^(2) =24`

Utilizați FOIL
`(2y+6)(2y+6)=4y^(2)+12y+12y+36=4y^(2)+24y+36`

`4y^(2)+24y+36-4y^(2)=24`

`24y+36=24`

`24y=-12`

`y= -(1)/(2)`



`a=x+2y+(x+2y)^(2)+(x+2y)^(3)+(x+2y)^(4)`

`a=(2y+6)+2y+((2y+6)+2y)^(2)+((2y+6)+2y)^(3)+`
`((2y+6)+2y)^(4)`


`a=(2(-1/2)+6)+2(-1/2)+((2(-1/2)+6)+2(-1/2))^(2)+`
`((2(-1/2)+6)+2(-1/2))^(3)+((2(-1/2)+6)+2(-1/2))^(4)`


`a=(-1+6)-1+((-1+6)-1)^(2)+((-1+6)-1)^(3)+((-1+6)-1)^(4)`

`a=5-1+(5-1)^(2)+(5-1)^(3)+(5-1)^(4)`

`a=4+4^(2)+4^(3)+4^(4)`

`a=4+16+64+256`

`a=240`