What are two consecutive integers whose square roots are also consecutives integers?
0 and 1
Thank you for helping me Rom how do you know that its 0 and 1....
To find the consecutive integers with consecutive integer square roots, we can start by assigning variables. Let's assume the first integer is represented by "x", and the second consecutive integer is represented by "x + 1".
Next, we can represent the square root of the first integer as √x, and the square root of the second integer as √(x + 1).
For the square roots to be consecutive integers, we need to find values of "x" that satisfy the following equation:
√(x + 1) = √x + 1
Now, let's solve the equation:
Square both sides of the equation:
(x + 1) = (x + 1)^2
Expand the squared expression on the right side of the equation:
(x + 1) = x^2 + 2x + 1
Rearrange the equation:
x + 1 = x^2 + 2x + 1
Combine like terms on the right side:
x + 1 = x^2 + 2x + 1
Subtract (x + 1) from both sides:
0 = x^2 + 2x - x - 1 + 1
Combine like terms:
0 = x^2 + x
Rearrange the equation:
x^2 + x = 0
Factor the equation:
x(x + 1) = 0
Now we have two possible solutions:
x = 0 or x = -1
Since we are looking for consecutive positive integers, we choose x = 0.
Thus, the consecutive integers are 0 and 1, and their square roots (0 and 1) are also consecutive integers.