Question

The sum of the squares of two positive consecutive odd numbers is 290. Find the average of
the numbers.​

Answer 1

Answer:

let the one number he x+1 and

other number he x+3

ATQ

(x+1)

$(x + 1) ^{2} + (x + 3) ^{2} = 290 \\ {x }^{2} + 2x + 1 + {x}^{2} + 6x + 9 = 290 \\ 2 {x }^{2} + 8x + 10 = 290 \\ 2( {x}^{2} + 4x + 5) = 290 \\ {x}^{2} + 4x + 5 = 145 \\ {x}^{2} + 4x + 5 - 145 = 0 \\ {x}^{2} + 4x - 140 = 0 \\ x(x + 14) - 10(x + 14) = 0 \\ (x - 10)(x + 14) = 0 \\ x - 10 = 0 \: \: or \: x + 14 = 0 \\ x = 10 \\ or \\ x = - 14(not \: \: possible)$

Therefore, x+1= 10+1=11

or

x+3= 10+3=13

Average of two numbers= 11+13/2= 12

Therefore, answer is 12