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:

let x, x+1, x+2 are the three consecutive numbers.

according to the question,

(x+1)^2+x(x+2)=199….[(x+1) is the middle one, x(x+2) is the product of the other two]

=>x^2+2x+1+x^2+2x=199

=> 2 x^2+4 x+1=199

=>2x^2+4x-198=0

using middle term factorization,

2x^2+(22x-18x)-198=0…[22–18=4, 22*18=198]

=> 2x^2+22x-18x-198=0

=>2x(x+11)-18(x+11)=0

=>(2x-18)*(x+11)=0

so, we have

2x-18=0 and x+11=0

x=18/2=9 and x=-11

so, the value of x are 9 & -11.

Answer 2

Answer:

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