Question 212506
Find two real numbers that have a sum of 6 and a product of 4.


Step 1.  Let x be one number


Step 2.  Let y be the other number


Step 3.  The problem statement gives us that x+y=6 or y=6-x


Step 4.  We're also give that


{{{xy=4}}}


Substitute {{{y=6-x}}}


{{{x(6-x)=4}}}


{{{6x-x^2=4}}}


Step 5.  Now use above equation to obtain a quadratic one.


Add {{{x^2-6x}}} to both sides of the equation so left side will = 0


{{{6x-x^2+x^2-6x=4+x^2-6x}}}


{{{0=x^2-6x+4}}}



Step 6. So now we have a quadratic equation, so we can use the quadratic formula given as


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


where a=1, b=-6 and c=4 for our example.  Follow steps below:



*[invoke quadratic "x", 1, -6, 4 ]



Step 7.  ANSWER:  The above steps give us two numbers :  5.2361 and 0.7639.  



You can check to see if these numbers add up to 6 and their products equal 4 as given by the problem.  


I hope the above steps were helpful.  Good luck in your studies!


Respectfully,
Dr J


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