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Random Interesting Patterns Followed by Square Numbers

Fill in the b...

Question

Fill in the blanks:
$11^{2} + 8^{2} + 3^{2} = 19^{2}$
$12^{2} + 2^{2} + 10^{2} = 14^{2}$
$14^{2} + 7^{2}$ + =

7^{2}, 11^{2}

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14^{2}, 21^{2}

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7^{2}, 19^{2}

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7^{2}, 21^{2}

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Solution

The correct option is D $7^{2}, 21^{2}$
From the pattern, the third number is the difference of the first two numbers.
The fourth number can be obtained by addition of the first two numbers.
Then, the missing numbers will be
$14^{2} + 7^{2} + 7^{2} = 21^{2}$
So, $7^{2}, 21^{2}$ are the missing numbers.

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1^{2} + 2^{2} + 2^{2} = 3^{2}

2^{2} + 3^{2} + 6^{2} = 7^{2}

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4^{2} + 5^{2} + . . . . . . = 21^{2}

5^{2} + . . . . . + 30^{2} = 31^{2}

6^{2} + 7^{2} + . . . . . . = . . . . . . . .

1^{2} + 2^{2} + 2^{2} = 3^{2}

2^{2} + 3^{2} + 6^{2} = 7^{2}

3^{2} + 4^{2} + 12^{2} = 13^{2}

4^{2} + 5^{2} +

= 21^{2}

5^{2} +

+ 30^{2} = 31^{2}

6^{2} + 7^{2} +

=

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