Question

the sum of squares of two consecutive odd positive integers is 970 find the integers using quadratic equation

Answer 1

Here is the required answer

Answer 2

Answer:

Required Odd numbers are 21 and 23.

Step-by-step explanation:

Let x and (x+2) are two consecutive odd positive integers.

According to the problem given,

x²+(x+2)²=970

=> x²+x²+4x+4-970=0

=> 2x²+4x-966=0

Divide each term by 2 ,we get

=> x²+2x-483=0

Splitting the middle term,we get

=> x²+23x-21x-483=0

=> x(x+23)-21(x+23)=0

=> (x+23)(x-21)=0

=> x+23 = 0 Or x-21 = 0

=> x = -23 Or x = 21

But x is positive odd number.

x = 21

Therefore,

Required Odd numbers are 21 and 23.

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