Question

Find two positive consecutive numbers such that sum of their squares is 61​

Answer 1

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Since they are consecutive numbers, one number is bigger than the other by 1.

So if 1 number is X the other number is X+1

Squares are X^2 and (X+1)^2

Sum of squares = X^2+(X+1)^2 = 61

X^2+X^2 + 2X +1 = 61

2X^2 + 2X =60

X^2 + X = 30

Here's a shortcut

Taking X common we get

X(X+1) = 30

Factors of 30 include 5 and 6

X(X+1) = 5x6

So X = 5 and X+1 = 6

Check:

Squaring 6^2 = 36 and 5^2 = 25

Sum = 36+25 = 61

Answer 2

Here Is Your Ans ⤵

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Let ,Two consecutive Positive numbers are X And X + 1

according To the Question ，

➡( X )² + ( X + 1 )² = 61

➡X² + X² + 1² + 2X = 61

➡2X² + 2X - 60 = 0

➡2X² + 12X - 10X - 60 = 0

➡2X ( X + 6 ) - 10 ( X + 6 ) = 0

➡(2X - 10 ) ( X + 6 ) = 0

➡X = 5 Or X = - 6 { Ignore Negative Value OF X }

Therefore , Two positive consecutive numbers are (5)² = 25 And ( 5 + 1 )² = 36

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