If the sum of the squares of two consecutive even numbers is $100$ , find the numbers.

6, 8

- 8, - 6

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- 6, 8

- 8, - 6

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- 6, - 8

6, - 8

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- 6, - 8

7, 8

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Solution

The correct option is C $6, 8$ or $- 8, - 6$
Let the numbers be x and x + 2. Then
$x^{2} + (x + 2)^{2} = 100$ or $x^{2} + x^{2} + 4 x + 4 = 100$
or $2 x^{2} + 4 x - 96 = 0$ or $x^{2} + 2 x - 48 = 0$
or $x^{2} + 8 x - 6 x - 48 = 0$ or $(x + 8 (x - 6) = 0$
i.e, $x = 6$ or $x = - 8$
Therefore, the numbers are 6, 8 or -8, -6.

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If the sum of the squares of two consecutive even numbers is 100, find the numbers.

The correct option is C 6,8 or −8,−6Let the numbers be x and x + 2. Thenx2+(x+2)2=100 or x2+x2+4x+4=100or 2x2+4x−96=0 or x2+2x−48=0or x2+8x−6x−48=0 or (x+8(x−6)=0i.e, x=6 or x=−8Therefore, the numbers are 6, 8 or -8, -6.

If the sum of the squares of two consecutive even numbers is $100$ , find the numbers.