Question

The difference f two numbers is 3. and their difference of their squares is 54. find oout the numbers.

Answer 1

${\huge{\underline{\underline {\sf {Correct\:Question:}}}}}$

The difference of two numbers is 3 and the difference of their squares is 54. find out the numbers.

${\underline {\rm{Given:}}}$

• The difference of two numbers is 3
• The product of their square is 54

${\underline {\rm{Find:}}}$

• The two numbers are = ?

${\underline {\rm{Solution:}}}$

Let the two numbers be x and y

According to the given question :

• x - y = 3
• ${x}^{2}-{y}^{2}$ = 54

We can take the difference of the numbers as

➵ y = x - 3

Substituting the values in the difference of the squares :-

➟ ${x}^{2}-{y}^{2}$ = 54

➟${x}^{2}-({x-3})^{2}$ = 54

➟${x}^{2}-({x}^{2} +6x -9)$ = 54

➟$6x -9$ = 54

➟$6x$ = 54 - 9

➟$6x$ = 63

➟$x = \dfrac {63}{6}$

➟$x = 10.5$

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✦Value of the numbers

x = 10.5

y = 10.5 + 3 = 13.5

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★Verification

Difference of the values

➵ y - x = 3

➵ 13.5 - 10.5 = 3

➵ 3 = 3

LHS = RHS

Hence proved!

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