What is the numbers whose sum is 31 and the product is 361
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Let the two numbers we have to find be x and y.
Now their sum is 31
=> x + y = 31
Their product is 361
=> x*y = 361
x + y = 31
=> x = 31 - y
(31 - y)*y = 361
=> 31y - y^2 = 361
=> y^2 - 31y + 361 = 0
So the numbers we get are complex:
x = 31/2 + sqrt ( 31^2 - 4*361) /2
=> x = 31/2 - i* sqrt 483 /2
and y = 31/2 + i sqrt 483/2
The numbers are 31/2 - i* sqrt 483 /2 and 31/2 + i*sqrt 483 /2
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Let the sum of the two numbers x1 and x2 = 31 and their product x1x2 = 361. We have to find the numbers x1 and x2.
So x1 and x2 are the roots of x^2-(x1+x2)x+x1x2 = 0, or
x^2-31x+361 = 0.
We know that the roots of the equation ax^2+bx+c = 0 is given by:x1 = {-b+sqrt(b^2-4ac)}/2a and
x2 = {-b+sqrt(b^2-4ac)}/2.
Here a = 1, b= -31 and c= 361.
So x1 = {-(-31) + sqrt{(-31)^2 - 4*361)}/2
x1 = {31+sqrt(-483)}/2
x2 = {31-sqrt(-483)}/2.
Therefore there are no real numbers whose sum is 31 and the product is 361. However there is solution in complex numbers.. So , x1 = {31+sqrt(-483)}/2 and x2 = {31-sqrt(-483)}/2 are the solutions.
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