Question

1. The sum of two numbers is 12 and difference of their squares is 12. The difference of the numbers is
(a) 2
(b) 0
(c) 1
(d) 3​

Answer 1

please mark it as brainliest answer for my effort

Answer 2

The difference between the numbers is (c) 1

Step-by-step explanation:

Given:

the sum of two numbers is 12,

the difference between their squares is 12

To find:

the difference in the numbers

Solution:

Let's assume the first number as x

Then according to given

The sum of the numbers is 12

x + second number = 12

∴ second number = 12-x

According to condition (II)

The difference between their squares is 12

∴ (12-x)² -x² = 12

Now using the formula (a-b)² for the bracket (12-x)²

(a-b)² = a²-2ab+b²

⇒  $[(12)\²-2(12)(x)+ (x)\²]- x\²= 12$

⇒ $[144- 24x + x\²]-x\² = 12$

opening the bracket

⇒ $144- 24x + x\²-x\² = 12$

The term x² gets eliminated and bringing the like terms together

⇒ $-24x = 12-144$

⇒  $- 24x=-132$

The negative sign gets eliminated

⇒ $x = \frac{132}{24}$

∴ $x = \frac{11}{2}$

The difference between the two numbers will be

= (12-x)-x

= 12 - 2x

= 12 - 2 (11/2)

= 12- 22/2

= 12-11

= 1

Thus, the difference between the numbers is 1

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