The square of one number is 23 less than the square of a second number. if the second number is 1 more than the first, what are the two numbers?

if x represents the smaller number, then which of the following quadratic equations represents the word problem?

a. x² + 23 = x² + 2x + 1
b. (x + 23)² = x² + 2x + 1
c. x² + 23 = x² + 1

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions