Question

How many distinct pairs of positive consecutive integers have a product less than 10,000?

Please explain it step-by-step

Answer 1

99.5

Explanation:

Let the consecutive positive integer be n , n+1

now, we know that there product is less then 10000

so, n(n+1) = 10000

So, the question asked " Less than 10,000 " so, we get the roots = (-100.50124999219 ), (99.501249992188)

n² + n - 10000 = 0

Let's solve this equation together!

n approximate number is 99.5.

Answer 2

Explanation:

Let the consecutive positive integer be x , x+1

now, we know that there product is less then 10000

so, x(x+1) = 10000

x² + x - 10000 = 0

On solving the quadractic equation,

we get the roots = (-100.50124999219 ), (99.501249992188)

since we are asked for less then 10000 we can approximate the answer to x = 99.5