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Squares and Square Roots
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08/08/2021 11:02 am
Topic starter
Using the given pattern, find the missing numbers.
12 + 22 + 22 = 32
22 + 32 + 62 = 72
32 + 42 + 122 = 132
42 + 52 + _2 = 212
5 + _ 2 + 302 = 312
6 + 7 + _ 2 = _ 2
1 Answer
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08/08/2021 11:04 am
Given, 12 + 22 + 22 = 32
i.e 12 + 22 + (1 × 2 )2 = ( 12 + 22 -1 × 2 )2
22 + 32 + 62 =72
∴ 22 + 32 + (2 × 3 )2 = (22 + 32 -2 × 3)2
32 + 42 + 122 = 132
∴ 32 + 42 + (3 × 4 )2 = (32 + 42 – 3 × 4)2
42 + 52 + (4 × 5 )2 = (42 + 52 – 4 × 5)2
∴ 42 + 52 + 202 = 212
52 + 62 + (5 × 6 )2 = (52+ 62 – 5 × 6)2
∴ 52 + 62 + 302 = 312
62 + 72 + (6 × 7 )2 = (62 + 72 – 6 × 7)2
∴ 62 + 72 + 422 = 432