How do you solve X^2-6x+11-x=y-(y+1)? My results show there are two answers for each coordinate, and both values work for the equation, but the answer says only one coordinate work, what do I do?

Answer 1

If the equation given is meant to be x² − 6x + 11 − x = y − (y + 1), then

simplification of left and right sides gives x² − 7x + 11 = y − y − 1 or

x² − 7x + 11 = − 1 or the quadratic equation x² − 7x + 12 = 0.

Seeking 2 numbers that add to 7 and multiply to 12 will lead to 3 and 4

which enables (x − 3) × (x − 4) or x² − 7x + 12 = 0 with the solution set

for x as {3,4}.

4 and 3 are also gained as roots of x² − 7x + 12 = 0 by way of

x = {-(-7) + √[(-7)² − (4×1×12)]} ÷ (2 × 1) which gives 4.

x = {-(-7) − √[(-7)² − (4×1×12)]} ÷ (2 × 1) which gives 3.

To be a differential equation, the given equation should

contain differential terms such as dy or dx and derivative

terms such as dy/dx, d²y/dx², y', or y''.