Question

Two numbers differ from 4and the products are 96find the number

Answer 1

Given

Two numbers differ from 4 and the products are 96

To find

Find the numbers

Solution

Let the numbers be x and y

According to the given condition

• x - y = 4 --(i)
• xy = 96 -----(ii)

from (i)

=> x - y = 4

=> x = 4 + y

Putting the value of x in equation (ii)

=> xy = 96

=> (4+y)y = 96

=> 4y + y² = 96

=> y² + 4y -96 = 0

Solve this by splitting middle term

=> x² -12x +8x -96 = 0

=> x(x-12)+8(x-12) = 0

=> (x-12)(x+8) = 0

Either

x = 12 or x = -8

By substitution method

By substitution methodsubstitute the both value value of x in equation (i)

In case : 1

if x = 12

=> x - y = 4

=> 12 - y = 4

=> 12-4 = y

=> y = 8

In case : 2

if x = -8

=> x - y = 4

=> -8 - y = 4

=> -8 - 4 = y

=> y = -12

Required numbers in case : 1

x = 12 and y = 8

Required numbers in case : 2

x = -8 and y = -12

Answer 2

$\huge\underline\mathrm{GivEn:-}$

$\longrightarrow$Two numbers differ from 4and the products are 96

$\huge\underline\mathrm{To Find:-}$

$\longrightarrow$ find the numbers =?

$\huge\underline\mathbb{SOLUTION:-}$

Let the two numbers be 'x' and 'y'.

According to question :-

$\longrightarrow$ x - y = 4 ___1)

and,

$\longrightarrow$ xy = 96 ___2)

From equation 1).

$\implies$ x - y = 4

$\implies$ x = 4 + y

➡ Put the value of 'x' in equation 2)

$\longrightarrow$ (4 + y)y = 96

$\longrightarrow$ 4y + y² = 96

$\longrightarrow$ y² + 4y - 96 = 0

$\longrightarrow$ y² + (12-8)y - 96 =0

$\longrightarrow$ y² + 12y - 8y - 96 =0

$\longrightarrow$ y(y + 12) -8(y + 12) =0

$\longrightarrow$ (y - 8) =0

$\longrightarrow$ (y + 12) =0

y = -12

y = 8

➡ Put the value of y = 8 in equation 1).

$\longrightarrow$ x - 8 = 4

$\longrightarrow$ x = 4 + 8

$\longrightarrow$ x = 12

➡ Put the value of y = -12 in equation 1)

$\longrightarrow$ x -(-12) = 4

$\longrightarrow$ x + 12 = 4

$\longrightarrow$ x = 4-12

$\longrightarrow$ x = -8

• Hence the two numbers are '12' and '8' in case 1)

and

the two numbers are -12 and -8 in case 2)

$\huge\underline\mathbb{THANKS...}$