Question

Find two consecutive positive odd numbers whose squares have the sum 71 ( Quadratic Equations )​​

Answer 1

Step-by-step explanation:

Let one of the odd positive integer be x

then the other odd positive integer is x+2

their sum of squares

=x

2

+(x+2)

2

=x

2

+x

2

+4x+4

=2x

2

+4x+4

Given that their sum of squares = 290

2x

2

+4x+4=290

2x

2

+4x=286

2x

2

+4x−286=0

x

2

+2x−143=0

x

2

+13x−11x−143=0

x(x+13)−11(x+13)=0

(x−11)=0,(x+13)=0

Therfore ,x=11or−13

We always take positive value of x

So , x=11 and (x+2)=11+2=13

Therefore , the odd positive integers are 11 and 13