Question

Find two consecutive positive integers sum of whose square is 25

Answer 1

Answer:

3 and 4

Step-by-step explanation:

Let the required numbers be x and x+1.

Given: x^2 + (x+1)^2 = 25

2x^2 + 2x - 24 = 0

Divide the equation by 2

We get,

x^2 + x - 12 = 0

i.e. x^2 + 4x - 3x - 12 = 0

i.e. x(x + 4) - 3(x + 4) = 0

(x + 4) (x - 3) = 0

x = - 4 or x = 3

Rejecting x = -4, we get the given consecutive positive integers as

x = 3 and x + 1 = 3 + 1 = 4

3^2+4^2=25

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