Question

Find two consecutive natural number, sum of whose squares is 365.​

Answer 1

Let the first number = x

Then the second number = x+1

According to the question ,

(x)²+(x+1)²= 365

x²+x²+1+2x = 365

2x²+2x+1 = 365

2x²+2x = 364

2x²+2x-364 = 0

2x²-26x +28 x - 364 = 0

2x(x-13)+ 28(x-13)

(x-13)(2x+28) = 0

x-13 => x = 13

2x+28 => x = -28/2

But the value of x can't be negative so x = 13

x+1 = 13+1 = 14

The required numbers are = 13 and 14

Answer 2

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