Question

Sum of the two numbers is 14 and difference between there square is 56 .If x and y are the numbers. What is the difference between the numbers? Find the numbers

Answer 1

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

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$\large{\green{\underline \bold{\tt{Given :-}}}}$

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• Sum of the two numbers is 14

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• Difference between their square is 56

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• x and y are the numbers

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$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

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• Difference between the numbers

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• The numbers

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

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Given that the numbers are x & y and sum of the two numbers is 14

Given that the numbers are x & y and sum of the two numbers is 14$\:\:$

So,

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➜ x + y = 14 -------- (1)

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Also given that, difference between their square is 56

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➜ x² - y² = 56

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➠ a² - b² = (a + b)(a - b)

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Here,

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• Let a = x
• Let b = y

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➜ x² - y² = (x + y)(x - y) = 56

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➜ (x + y)(x - y) = 56 ------- (2)

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⟮ Putting x + y = 14 from (1) to (2) ⟯

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➜ (x + y)(x - y) = 56

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➜ (14)(x - y) = 56

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➜ $\sf x - y = \dfrac { 56 } { 14 }$

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➨ x - y = 4 ------- (3)

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• Hence the difference between the numbers is 4

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⟮ Adding equation (1) & (3) ⟯

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➜ x + y + x - y = 14 + 4

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➜ 2x = 18

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➨ x = 9 ------ (4)

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• Hence the first number is 9

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⟮ Putting x = 9 from (4) to (3) ⟯

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➜ x - y = 4

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➜ 9 - y = 4

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➜ y = 9 - 4

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➨ y = 5

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• Hence the second number is 5

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Answer 2

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

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Sum of the two numbers is 14

$\:\:$

• Difference between their square is 56

$\:\:$

• x and y are the numbers

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• Difference between the numbers

$\:\:$

• The numbers

$\:\:$

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

$\:\:$

Given that the numbers are x & y and sum of the two numbers is 14

Given that the numbers are x & y and sum of the two numbers is 14$\:\:$

So,

$\:\:$

➜ x + y = 14 -------- (1)

$\:\:$

Also given that, difference between their square is 56

$\:\:$

➜ x² - y² = 56

$\:\:$

➠ a² - b² = (a + b)(a - b)

$\:\:$

Here,

$\:\:$

Let a = x

Let b = y

$\:\:$

➜ x² - y² = (x + y)(x - y) = 56

$\:\:$

➜ (x + y)(x - y) = 56 ------- (2)

$\:\:$

⟮ Putting x + y = 14 from (1) to (2) ⟯

$\:\:$

➜ (x + y)(x - y) = 56

$\:\:$

➜ (14)(x - y) = 56

$\:\:$

➜ $\sf x - y = \dfrac { 56 } { 14 }$

$\:\:$

➨ x - y = 4 ------- (3)

$\:\:$

Hence the difference between the numbers is 4

$\:\:$

⟮ Adding equation (1) & (3) ⟯

$\:\:$

➜ x + y + x - y = 14 + 4

$\:\:$

➜ 2x = 18

$\:\:$

➨ x = 9 ------ (4)

$\:\:$

Hence the first number is 9

$\:\:$

⟮ Putting x = 9 from (4) to (3) ⟯

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➜ x - y = 4

$\:\:$

➜ 9 - y = 4

$\:\:$

➜ y = 9 - 4

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➨ y = 5

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Hence the second number is 5

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