Question

6. One is added to the product of two consecutive positive even numbers. Show that the result is a square number.​

Answer 1

Answer:

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

According to question:

2x(2x+2)=168

⇒4x

2

+4x−168=0

⇒x

2

+x−42=0

⇒x

2

+7x−6x−42=0

⇒x(x+7)−6(x+7)=0

⇒(x+7)(x−6)=0

⇒x=−7,x=6

But x cannot be negative.

∴ If x=6 then 2x=12 and 2x+2=14

∴ Two consecutive even numbers are 12 and 14

Step-by-step explanation:

Hope it's help you!!!

Answer 2

Answer:

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

According to question:

2x(2x+2)=168

⇒4x

2 +4x−168=0

⇒x

2 +x−42=0

⇒x

2 +7x−6x−42=0

⇒x(x+7)−6(x+7)=0

⇒(x+7)(x−6)=0

⇒x=−7,x=6

But x cannot be negative.

∴ If x=6 then 2x=12 and 2x+2=14

∴ Two consecutive even numbers are 12 and 14