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
X² + (X+2)² = 394
X² + X² + 4X + 22 = 394
2X² + 4X + 4 = 394     
X² +2X =(394 - 4)/2
X² + 2X = 195
X²+2X - 195 = 0
X² + 15X - 13X -195 = 0    .
X( X + 15 ) - 13( X + 15 ) = 0
( X + 15 ) ( X - 13 )

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x+15=0
x=-15
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x-13=0
x=+13
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We are taking the value of x to be 13 as it is a positive number.
And (x+2)=13+2  =15

Hence, the two consecutive numbers are 13,15.

Answer 2

Hi friend!!

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

As per 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,,...