Two positive real numbers have a sum of 5 and product of 5. Find the number.?

Let

X = first number

Y = second number

X + Y = 5 -- Equation 1

XY = 5 -- Equation 2

From Equation 2, since Y = 5/X and substituting this into Equation 1,

X + 5/X = 5

Simplifying the above,

X^2 + 5 = 5X

X^2 - 5X + 5 = 0

Solving for the roots of the above using the quadratic formula,

X = [5 ± sqrt(5)]/2

and solving for Y,

Y = 5/X = 5/[5 ± sqrt(5)]/2

Y = 10/[5 ± sqrt(5)]

Hope this helps.

Find two equations. To do this, asssign a random variable to your unknowns.

So two numbers sums equal 5? Then x+x=5 or 2x=5

Their products? y*y=5 or y^2=5

Solve for the equation and you will see the answer is 2 and 1/2

the two numbers are 2.5 + sqrt(5) / 2 and 2.5 - sqrt(5) / 2

two equations:

x + y = 5

xy = 5

rearranging the first equation:

y = 5 - x

sub into second equation

x(5 - x) = 5

5x - x^2 = 5

x^2 - 5x + 5 = 0

using the quadratic formula with a = 1, b = -5, and c = 5:

x = [5 +/- sqrt(5^2 - 4(5))] / 2

x = [5 +/- sqrt(5)] / 2, yielding the two positive numbers:

2.5 + sqrt(5) / 2 and 2.5 - sqrt(5) / 2

check: sum = 5 yep

(2.5 + sqrt(5)/2)(2.5 - sqrt(5) / 2) =

2.5^2 - 5/4 = 6.25 - 1.25 = 5 yep

Since the numbers in question add up to 5, call them x and 5-x. Then make their product equal to 5:

x(5-x) = 5

Multiply it out and solve:

5x-x² = 5

x²-5x+5 = 0

x = (5±√(25-20)) / 2

x = 2.5±(√5)/2

Therefore, the numbers are approximately 1.4 and 3.6.

Let the numbers be x and y.

x + y = 5

x*y = 5

Take the first equation:

x + y = 5

Subtract x from both sides:

y = 5 - x

Plug into other equation:

x(5 - x) = 5

Distribute x:

5x - x² = 5

Add x² and subtract 5x from both sides:

x² - 5x + 5 = 0

Apply the quadratic formula to solve for x:

x = [5 ± √((-5)² - 4(1)(5))]/((2)(1))

x = [5 ± √(25 - 20)]/2

x = [5 ± √(5)]/2

Find y:

y = 5 - x

y = 5 - [5 ± √(5)]/2

y = 10/2 - [5 ± √(5)]/2

y = [5 ± √(5)]/2

So x=y=[5 ± √(5)]/2

xy = 5....1

x+y = 5...2

x = 5/y

5/y + y = 5

5 + y^2 = 5y

y^2 -5y + 5 = 0

y1= 3.618

y2 = 1.381966

put y1 and y2 into 1

This is Impossible there is no solution.