Question

Two consecutives positive add numbers are such that the sum of their square is 130. Find two numbers:
(7 and 9)
(5 and 7)
(3 and 5)

Answer 1

Step-by-step explanation:

Let x be the positive odd number and the consecutive odd number be (x+2).

It is given that the sum of the squares of two consecutive numbers is 130, therefore,

(x)

2

+(x+2)

2

=130

⇒x

2

+x

2

+4+4x=130(∵(a+b)

2

=a

2

+b

2

+2ab)

⇒2x

2

+4x+4−130=0

⇒2x

2

+4x−126=0

⇒2(x

2

+2x−63)=0

⇒x

2

+2x−63=0

⇒x

2

+9x−7x−63=0

⇒x(x+9)−7(x+9)=0

⇒(x−7)=0,(x+9)=0

⇒x=7,x=−9

Since it is given that x is a positive odd number, thus x=7.

Now, x+2=7+2=9

Hence, the two consecutive positive odd numbers are 7 and 9.