Question

Find two consecutive odd positive integers ,sum of whose squares is 290​

Answer 1

Answer:

11 and 13

Step-by-step explanation:

Let the odd positive integers be x and x+2,

Given,

Sum of their squares is 290

Therefore,

x²+(x+2)² = 290

x²+x²+4+4x = 290

2x²+4x=286

2x²+4x-286=0

Dividing by 2,

x²+2x-143=0

On adding we should get +2 and On multiplying we should get -143

The factors are -11 and 13

On splitting the middle term,

x²-11x+13x-143=0

x(x-11)+13(x-11)=0

(x-11)(x+13)=0

x-11=0 or x+13=0

x=11 or x=-13

Since positive integers are asked -13 can't be a solution

So, x=11

Therefore,

The consecutive odd positive integers are 11 and 13.

Hope it helps..❤️

Answer 2

Answer:

The answer is 11 and 13

Step-by-step explanation:

121+169=290