Question

sequence of even number? one added to the product of two consecutive even number give 289 .from a second degree equation to solve problem?​

Answer 1

Answer:

Let two consecutive even number be x and x+2.

According to the question,

⇒ x

2

+(x+2)

2

=340

⇒ x

2

+x

2

+4x+4=340

⇒ 2x

2

+4x+4=340

⇒ 2x

2

+4x+4−340=0

⇒ 2x

2

+4x−336=0

⇒ x

2

+2x−168=0

⇒ x

2

+14x−12x−168=0

⇒ x(x+14)−12(x+14)=0

⇒ (x+14)(x−12)=0

⇒ x+14=0 and x−12=0

⇒ x=−14 and x=12

∴ One number is 12

⇒ Other number =12+2=14

⇒ Required product =12×14=168