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Using the given pattern, find the missing numbers. 1^2 + 2^2 + 2^2 = 3^2 ; 2^2 + 3^2 + 6^2 = 7^2

Q.6 Using the given pattern, find the missing numbers.

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}+\;-\; ^{2} = 21^{2}

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

6^{2}+7^{2}+-^{2}= -^{2} 

Answers (1)
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Patter is clearly visible.

First two numbers and the last two numbers are the consecutive numbers.

Moreover, the third number is obtained when the first is multiplied with the second number.

So required numbers can be found. 

i.e., 4 \times 5 = 20                and           6 \times 7 = 42

hence         4^{2} + 5^{2} + 20^{2} = 21^{2}

and             5^{2} + 6^{2} + 30^{2} = 31^{2}

and              6^{2} + 7^{2} + 42^{2} = 43^{2}   

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