Question

Three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46, find the integers.​

Answer 1

Step-by-step explanation:

⇒ Let there consecutive positive integers are x,x+1,x+2.

According to the question,

⇒ x

2

+(x+1)(x+2)=46

⇒ x

2

+x

2

+2x+x+2=46

⇒ 2x

2

+3x+2−46=0

⇒ 2x

2

+3x−44=0

⇒ Here, a=2,b=3 and c=44

⇒ x=

2a

−b±

b

2

−4ac

⇒ x=

2(2)

−3±

(3)

2

−4(2)(−44)

⇒ x=

4

−3±

361

⇒ x=

4

−3±19

⇒ x=

4

−3+19

and x=

4

−3−19

∴ x=

4

16

and x=

4

−22

∴ x=4 and x=

2

−11

⇒ Here, there is only one integer which is 4.

∴ Smallest integer is 4

hope it will help u