Question

The difference of two number is 12 and product of 4

Answer 1

Solution

Given :-

• difference of two number is 12
• product of 4

Find :-

• These Number

Explanation

Let,

• First Number be = x
• Second Number be = y

A/C to question,

==> x - y = 12 ----------(1)

again,

==> x y = 4 -------------(2)

Using Formula

★ ( x + y) = √[(x-y)² + 4xy]

Keep Value by equ(1) & equ(2)

==> x + y = √[12² + 4 * 4 ]

==> x + y = √[144+16]

==> x + y = √160

==> x + y = 4√10 ------------(3)

Add equ(1) & (3)

==> 2x = 12 + 4√10

==> x = 2(6+2√10)/2

==> x = (6+2√10)

Keep Value of x in equ(1)

==> (6+2√10) - y = 12

==> y = 6 +2√10 - 12

==> y = -6 + 2√10

Hence

• First Number = ( 6 + 2√10)
• Second Number = (-6 + 2√10)

______________

Answer 2

Answer :

The two numbers are 6+2√10, -6+2√10

Step by step explanation :

According to the question the two numbers be x and y

Difference of two numbers =12 And .................(1)

Product of two numbers = 4. ........................(2)

So the equations are x-y=12 and x*y=4

We know that, (x+y)=√(x-y)²+4xy

Substitute the values

(x+y)=√(12)²+4*4

(x+y)=√144+16

(x+y)=√160

(x+y)=4√10 ..................(3)

So, x+y=4√10

x-y=12

-----------------

2x=12+4√10

x=6+2√10

Keep the value 0f x to get

x-y=12

6+2√10-y=12

6+2√10-12=y

y=-6+2√10