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

$\Large{\underline{\underline{\mathfrak{\bf{\red{Solution}}}}}}$

$\Large{\underline{\mathfrak{\bf{\orange{Given}}}}}$

• The sum of two numbers is 12
• difference of their squares is 12

$\Large{\underline{\mathfrak{\bf{\orange{Find}}}}}$

• Difference of Numbers

$\Large{\underline{\underline{\mathfrak{\bf{\red{Explanation}}}}}}$

Let,

• First number = x
• Second number = y

A/C to question,

(The sum of two numbers is 12)

➠ x + y = 12 ------------(1)

And, Again

(difference of their squares is 12)

➠ x² - y² = 12----------(2)

Using Formula

★ (a² - b²) = (a-b)(a+b)

So, by equ(2)

➠ (x-y)(x+y) = 12

Keep Value by equ(1)

➠ x - y = 12/12

➠ x - y = 1 ----------(3)

Now, add equ(1) & (2)

➠ 2x = 12 + 1

➠ 2x = 13

➠ x = 13/2

keep Value of x in equ(3)

➠ 13/2 - y = 1

➠ y = 13/2 - 1

➠ y = (13-2)/12

➠ y = 11/12

$\Large{\underline{\underline{\mathfrak{\bf{\red{Hence}}}}}}$

• Value of x = 13/2
• Value of y =11/2

_________________

Now , Calculate difference of these numbers

➠ x - y = 13 /2 - 11/2

➠ x - y = ( 13 - 11)/2

➠ x - y = 2/2

➠ x - y = 1

$\Large{\underline{\underline{\mathfrak{\bf{\red{Since}}}}}}$

• Difference of these number will be 1,

So, Our answer will be option number (c).

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