Question

sum of the squares of two consecutive natural odd numbers is greater by 2 than 16 time there sum.find the numbers​

Answer 1

let the first odd number be x

second odd no. consecutive to x = x+2

ATQ,

x^2 +(x+2)^2 = 16( x+x+2) + 2

x^2 + x^2+4x+4 = 32x + 32 + 2

x^2 + x^2+4x+4 = 32x + 34

2x^2+ 4x+ 4 = 32x + 34

Dividing both sides by 2,

x^2 + 2x + 2 = 16x + 17

x^2 - 14x - 15 = 0

x^2 - 15x + x - 15 = 0

x(x-15) +1(x-15) = 0

(x+1)(x-15) = 0

x-15 = 0( since both are natural x= -1 is not valid)

x = 15

second no. = x+2 = 15+2= 17

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Answer 2

Answer:

the answer for the given problem is 15 and 17