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Alenkinab [10]
2 years ago
9

Find the TWO integers whos product is -12 and whose sum is 1​

Mathematics
2 answers:
kumpel [21]2 years ago
6 0

Answer:

\displaystyle( {x}_{1} , y_{1})   =(  - 3,4)\\ (x _{2}, y_{2})  = (4, - 3)

Step-by-step explanation:

we are given two conditions

  1. two integers whos product is -12
  2. two integers whos sum is 1

let the two integers be x and y respectively according to the first condition

\displaystyle xy =  - 12

according to the second condition:

\displaystyle x + y =  1

now notice that we have two variables therefore ended up with a simultaneous equation so to solve the simultaneous equation cancel x from both sides of the second equation which yields:

\displaystyle y =  1 - x

now substitute the got value of y to the first equation which yields:

\displaystyle x(1 - x) =  - 12

distribute:

\displaystyle x- {x}^{2}  =  - 12

add 12 in both sides:

\displaystyle x- {x}^{2}   + 12 = 0

rearrange it to standard form:

\displaystyle - {x}^{2}   +  x  + 12 = 0

divide both sides by -1:

\displaystyle {x}^{2}   -   x  -  12 = 0

factor:

\displaystyle ({x} + 3)(x - 4) = 0

by <em>Zero</em><em> product</em><em> </em><em>property</em> we acquire:

\displaystyle {x} + 3 = 0\\ x - 4= 0

solve the equations for x therefore,

\displaystyle {x}_{1}  =  - 3\\ x _{2} = 4

when x is -3 then y is

\displaystyle y _{1}=  1 - ( - 3)

simplify

\displaystyle y _{1}=  4

when x is 4 y is

\displaystyle y _{2}=  1 - ( 4)

simplify:

\displaystyle y _{2}=  - 3

hence,

\displaystyle( {x}_{1} , y_{1})   =(  - 3,4)\\ (x _{2}, y_{2})  = (4, - 3)

Deffense [45]2 years ago
4 0

Answer:

\rm Numbers = 4 \ and \ -3.

Step-by-step explanation:

Given :-

The sum of two numbers is 1 .

The product of the nos . is 12 .

And we need to find out the numbers. So let us take ,

First number be x

Second number be 1-x .

According to first condition :-

\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}

Hence the numbers are 4 and -3

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