Question

If x-2y=8 and x^2-4y^2=128, calculate the value of x+2y.

Answer 1

Step-by-step explanation:

x-2y=8

so, x=8+2y

substituting this value in eq. 2

we get,

${(8 + 2y)}^{2} - 4 {y}^{2} = 128 \\ 64 + 32y + {y}^{2} - 4 {y}^{2} = 128 \\ - 3 {y}^{2} + 32y + 64 - 128 = 0 \\ multiplying \: the \: whole \: equation \: with \: - 1 \: we \: get \\ 3 {y}^{2} - 32y + 64 = 0 \\ 3 {y}^{2} - 24y - 8y + 64 = 0 \\ 3y(y - 8) - 8(y - 8) = 0 \\ (y - 8)(3y - 8) = 0 \\ y = 8 \: or \: y = 8 \div 3$

for y=8

x=8+2×8

x=8+16

x=24

for y=8/3

x=8+2×(8/3)

x=8+16/3

x=(24+16)/3

x=40/3

Now the value of x+2y

for x=24 and y=8

24+8×2

24+16=40

for x=40/3 and y=8/3

x+2y=40/3 + 2×(8/3)

=40/3+16/3

=56/3

HOPE IT WILL HELP YOU