Question

Difference between two numbers is 4 and the difference between their squares is 80 .

Find the numbers ?​

Answer 1

Answer:

a= 12

b= 8

Step-by-step explanation:

a-b= 4------------ (1)

a^2- b^2 = 80 = (a+b)(a-b)

for the above

a+b = 20------------(2)

solve 1 and 2

we get

2a= 24

a= 12

b= 8

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Answer 2

Answer :-

Large number = x

Small number = y

Difference between two numbers is ==> 4

$\huge\boxed{x - y = 4}$

Difference between their Squares ==> 80

$\huge\boxed{x {}^{2} - y {}^{2} = 80}$

$\implies\bf \: (x + y)(x - y) = x {}^{2} - y {}^{2}$

$\implies\bf \: (x + y) \times 4 = 80$

$\implies\bf \: (x + y) = \frac{80}{4}$

$\huge\boxed{x + y = 20}$

$\implies\bf \: x + y = 20$

$\implies\bf \: x - y = 4$

$\implies\bf \: x = \frac{20 + 4}{2}$

$\implies\bf \: x = \frac{24}{2}$

$\huge\boxed{x = 12}$

$\implies\bf \: y = \frac{20 - 4}{2}$

$\implies\bf \: y = \frac{16}{2}$

$\huge\boxed{y = 8}$

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• Large number ==> x ==> 12

• Small number ==> y ==> 8

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