Question

Difference between two number's in 4and the difference between their squares is 80.Find the number

Answer 1

✬ Numbers = 12 & 8 ✬

Step-by-step explanation:

Given:

• Difference between two numbers is 4.
• Difference between squares of these number is 80.

To Find:

• What are the numbers ?

Solution: Let the numbers be x and y. Therefore,

➟ x – y = 4

➟ x = 4 + y................i

Now squaring these numbers

• One number = x²
• Second number = y²

A/q

$\implies{\rm }$ x² – y² = 80

$\implies{\rm }$ (4 + y)² – y² = 80

$\implies{\rm }$ 4² + y² + 2(4)(y) – y² = 80

$\implies{\rm }$ 16 + 8y = 80

$\implies{\rm }$ 8y = 80 – 16

$\implies{\rm }$ y = 64/8

$\implies{\rm }$ y = 8

So,

• x = 4 + 8 = 12

Hence, two numbers are 12 and 8.

[ Verification ]

➮ 12 – 8 = 4

and

➮ 12² – 8² = 80

➮ 144 – 64 = 80

$\large\bold{\texttt {Verified }}$

Answer 2

$\sf \underline{Given} :$

• Difference between two number's in 4

• the difference between their squares is 80

$\sf \underline{To \: Find} :$

• Find the number

$\sf \underline{Solution} :$

Let The number is x and Y

☯ $\underline{\boldsymbol{According\: to \:the\: question :}}$

$\sf \leadsto \: x \: - y \: = 4 \\ \\ \sf \leadsto \: x = 4 + y............(1) \\ \\ \sf \leadsto \: {x}^{2} - {y}^{2} = 80..............(2)$

$\sf \underline{ \underline {from \: equ \:( 2) \: } }:$

$\sf \leadsto \: x^2 - y^2 = 80..............(2)$

Substitute all values ;

$\sf \leadsto \: {x}^{2} - {y}^{2} = 80 \\ \\ \sf \leadsto \: {(4 + y})^{2} - {y}^{2} = 80\\ \\ \sf \leadsto \: {4}^{2} + \cancel{ {y}^{2} } + 8y - \cancel{{y}^{2}} = 80 \: \\ \\ \sf \leadsto 16 + 8y = 80 \\ \\ \sf \leadsto \: 8y = 80 - 16 \\ \\ \sf \leadsto \: 8y = 64 \\ \\ \sf \leadsto y = \: \cancel{\frac{64}{8} } \\ \\ \sf \leadsto \: y = 8$

substitute the value of y in Equ. 1

$\sf \leadsto \: x = 4 + y \\ \\ \sf \: \leadsto \: \: x = 4 + 8 \\ \\ \sf \leadsto \: x = 12$

Hence the value of number x = 12 and Y

y = 8.