Question

The difference between the squares of two consecutive odd numbers is 56. Find the
numbers.​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large\underline{\green{\bf Given :-}}$

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• The difference between the squares of two consecutive odd numbers is 56

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$\large\underline{\red{\bf To \: Find :-}}$

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• The numbers

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$\large\underline{\orange{\bf Solution :-}}$

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• Let the first odd number be "x"

• Then the consecutive odd number will be "x + 2"

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$\underline{\bold{\texttt{Consecutive odd number :}}}$

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➠ x + 2 ⚊⚊⚊⚊ ⓵

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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The difference between the squares of two consecutive odd numbers is 56

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➜ (x + 2)² - x² = 56

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➜ x² + 2² + 2(x)(2) - x² = 56

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➜ x² + 4 + 4x - x² = 56

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➜ 4x + 4 = 56

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➜ 4x = 56 - 4

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➜ 4x = 52

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➨ x = 13

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• Hence the first odd number is 13

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⟮ Putting x = 13 in ⓵ ⟯

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➜ x + 2

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➜ 13 + 2

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➨ 15

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• Hence the consecutive odd number is 15

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∴ The numbers are 13 & 15

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