Question

is the numbers difference of two numbers is 3 and the difference of their squares is 57 the larger number is

Answer 1

Answer:

Larger number = 11

Step-by-step explanation:

Given--->

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Difference of two numbers is 3 and difference of their squares is 57

To find --->

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Value of larger number

Solution--->

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Let larger number be x and smaller number be y

ATQ

Difference of two numbers = 3

=> x - y = 3 ---------------(1)

ATQ

Difference of their squares = 57

=> x² - y² = 57

We have an identity a² - b² =

(a + b ) ( a - b)

Applying it here we get

=> (x + y ) ( x - y ) = 57

Putting x - y = 3

=> ( x + y ) ( 3 ) = 57

=> ( x + y ) = 57 / 3

=> x + y = 19

=> x + y = 19 --------------(2)

=> y = 19 - x

Putting y = 19 - x in equation (1)

=> x - ( 19 - x ) = 3

=> x - 19 + x = 3

=> 2x = 3 + 19

=> 2 x = 22

=> x = 22/ 2

=> x = 11

Putting x = 11 in equation (2)

x + y = 19

=> 11 + y = 19

=> y = 19 - 11

=> y = 8

Larger number = x = 11

Answer 2

Given:

The difference between two numbers=3

The difference of their squares=57

To find:

larger number

Explanation:

$\sf let \: the \: numbers \: be \: x \: and \: y$

According to the given information,

assume x>y

So

$\longrightarrow \sf x - y = 3 \\ \\\longrightarrow \sf x = y + 3 \\ \\ \longrightarrow \sf y = x - 3........(1)$

And also

$\longrightarrow \sf {x}^{2} - {y}^{2} = 57$

Substituting the value of y from equation (1)

$\longrightarrow \sf {x}^{2} - {(x - 3)}^{2} = 57 \\ \\ \longrightarrow \sf {x}^{2} - ( {x}^{2} + {3}^{2} - 2(3)(x)) = 57$

$\boxed{\tt (a-b)^2=a^2+b^2-2ab}$

$\longrightarrow \sf {x}^{2} - {x}^{2} - 9 + 6x = 57 \\ \\ \longrightarrow \sf 6x - 9 = 57 \\ \\ \longrightarrow \sf 6x = 57 + 9 \\ \\ \longrightarrow \sf 6x = 66 \\ \\ \longrightarrow \boxed {\sf \: x = 11}$

We assumed that x>y

so the larger number is 11

Smaller number=11-3=8