Question

1+y^2-2y= 64-16b+b^2= 9x^2-24xy+16y^2=

Answer 1

1+y²-2y=(y-1)²

64-16b+b²=(8-b)²

9x^2-24xy+16y²=(3x-4y)²

Answer 2

To solve the given system of equations:

1 + y^2 - 2y = 64 - 16b + b^2 ... (Equation 1) 64 - 16b + b^2 = 9x^2 - 24xy + 16y^2 ... (Equation 2)

Let's solve Equation 1 for y:

Rearranging Equation 1, we have: y^2 - 2y + 1 = 64 - 16b + b^2 y^2 - 2y - (64 - 16b + b^2 - 1) = 0 y^2 - 2y - 63 + 16b - b^2 = 0

Now, let's solve Equation 2 for x:

Rearranging Equation 2, we have: 9x^2 - 24xy + 16y^2 = 64 - 16b + b^2 9x^2 - 24xy + 16y^2 - (64 - 16b + b^2) = 0 9x^2 - 24xy + 16y^2 - 64 + 16b - b^2 = 0

Now we have two equations:

y^2 - 2y - 63 + 16b - b^2 = 0 ... (Equation 3) 9x^2 - 24xy + 16y^2 - 64 + 16b - b^2 = 0 ... (Equation 4)

To solve for x and y, we need to solve this system of equations simultaneously. However, we don't have enough information to find unique solutions. We need at least one more equation to find the values of x and y.