Question

The sum of the squares of two consecutive odd numbers is 394. Find the numbers.

Answer 1

Let the two consecutive odd numbers be x and x+2

As per the question,

x²+(x+2)² = 394

x²+x²+4x+4 = 394

2x²+4x = 394-4

2x²+4x = 390

2(x²+2x) = 390

x²+2x = 390/2

x²+2x-195 =0

x²+15x-13x-195 = 0

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

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

x+15 = 0 ; x = -15

x-13 = 0 ; x = 13

If x = -15,then the other number is

x+2 = -15+2 = -13

If x = 13 then the other number is

x+2 = 13+2 = 15

Therefore, the numbers are

» -15 and -13

» 13 and 15

We can take even negative numbers because square of a negative number is positive.

Hope it helps you:)

Answer 2

SOLUTION :  

Let the one consecutive odd numbers be (x + 1) and other consecutive odd numbers be (x + 3).

A .T.Q

(x + 1)² + (x + 3)² = 394

x² + 1 + 2x + x² + 9 + 6x = 394

[(a + b)² = a² + b² + 2ab ]

2x² + 8x + 10 = 394

2x² + 8x + 10 - 394 = 0

2x² + 8x - 384 = 0

2(x² + 4x - 192) = 0

x² + 4x - 192 = 0

x² + 16x - 12x  - 192 = 0

[By middle term splitting]

x(x + 16) - 12(x + 16) = 0

(x + 16) (x - 12) = 0

(x + 16)  = 0  or (x - 12) = 0

x = - 16 or x = 12  

Case 1 :  

When x = 12, then First odd number (x + 1) = 12 + 1 = 13

Second odd  number (x + 3) = 12 + 3 = 15.

Case 2 :  

When x = - 16, then First odd number (x + 1) = - 16 + 1 = - 15

Second odd  number (x + 3) = - 16 + 3 = - 13

Hence, the two numbers be (13, 15) & ( -13 , - 15).

HOPE THIS  ANSWER WILL HELP YOU..