Question

find the two quality concept in natural numbers sum of whose squares is 85​

Answer 1

Answer:

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Answer 2

Answer:

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Let the two consecutive natural numbers be ‘x’ and ‘x + 1’

⇒ Given that the sum of their squares is 85.

Then by hypothesis, we get

2 + ( + 1)2 = 85

⇒ 2 + 2 + 2 + 1 = 85

⇒ 22 + 2 + 1 − 85 = 0

⇒ 22 + 2 + 84 = 0 ⇒ 2 [2 + − 42 ] = 0

⇒ 2 + 7 - 6 - 42 = 0 [by the method of factorisation]

⇒ ( + 7) - 6( + 7) = 0

⇒ ( - 6)( + 7) = 0

⇒ = 6 or = 7

Case i: if x = 6 x + 1 = 6 + 1 = 7

Case ii: If x = 7 x + 1 = -7 + 1 = -6

∴ The consecutive numbers that the sum of this squares be 85 are 6,7 and -6, -7.