Question

there are three consecutive positive integers such that the square of the middle one increased by the product of other two gives 199 find the integer​

Answer 1

Answer:

Explanation:

As the Question stats:-

There are three consecutive positive integers :- let us assume three consecutive positive integers (x-1), x, (x+1).

Square of mid term increased by the product of other two ( side ) terms gives 199.

Square of mid term : x^2

Product of side terms : (x-1)×(x+1) =(x^2) - 1 [according to the formula of a^2 - b^2 =(a+b)(a-b)]

So, x^2 increased by (x^2)-1 gives 199.

x^2 + x^2 - 1 = 199

2x^2 - 1 = 199

2x^2 = 199+1 = 200

x^2 = 200/2 = 100

x = 10

So the integers; ( x-1) , x, (x+1)

=> 10–1, 10, 10+1

=> 9, 10, 11