Question

Find two consecutive odd numbers whom sum of square is 130.​

Answer 1

Solution:-

Let the two Odd Consecutive Numbers be ( 2x + 1) and ( 2x +3).

A.T.Q.

=) ( 2x + 1)² + ( 2x + 3)² = 130

=) 4x² + 1 + 4x + 4x² + 9 + 12x = 130

=) 8x² + 16x + 10 - 130 = 0

=) 8 ( x² + 2x - 8) = 0

=) x² + 2x - 8 = 0

=) x² + ( 4 - 2)x - 8 = 0

=) x² + 4x - 2x - 8 = 0

=) x ( x + 4) -2 ( x + 4) = 0

=) ( x + 4) ( x - 2)

=) [ x = -4 ] and [ x = 2 ].

Hence,

The Two Consecutive Odd Numbers are;

For [ x = -4 ]

( x + 3) = ( -4 + 3 ) = -1

( x + 5) = ( -4 + 5) = 1

For [ x = 2]

( x + 3) = 5

( x + 5) = 7

Answer 2

$\huge{\mathfrak{Solution:-}}$

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Let x be an odd number

Then the second number will be x+2

According to the question,

x² + (x+2)² = 130

x² + x² + 4x + 4 = 130

2x² + 4x + 4= 130

2x²+4x + 4 - 130 = 0

2x² + 4x - 126 = 0

Dividing the equation by 2

x² + 2x - 63 = 0

x² + 9x - 7x - 63 = 0

x(x+9) -7(x+9) = 0

(x+9)(x-7) = 0

This implies

x = -9

x = 7

Since, x is a positive integer, x = -9 has to be ignored,

Hence, x = 7

x + 2 = 9

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$\tt{\red{Hence\:the\:two\:numbers\:are:-}}$

$\huge{\green{7\:and\:9}}$

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