Question

Find two consecutive odd natural numbers, the sum of whose squares is 394.

Answer 1

Answer:

Step-by-step explanation:

Let the numbers be x and (x+2).

x²+(x+2)²=394.

x²+x²+4x+4=394.

2x²+4x+4=394.

2x²+4x-390=0.

2(x²+2x-195)=0.

x²+2x-195=0/2.

x²+2x-195=0.

x²+15x-13x-195=0.

x(x+15)-13(x+15)=0.

(x-13)(x+15)=0.

x=+13,-15.

Two no. are +13 and +15 or - 15 and - 13.

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Answer 2

let 2 consecutive no. be x and x+2.

x2+(x+2)2 =394

x2+x2+4x+4=394

(2x2+4x-390=0)÷2

x2+2x-195=0

x(x+15)-13(x+15)=0

(x-13)(x+15)=0

x=13,x=-15