By minimizing(derivation) the equation and solving the equation by equating to zero , the resultant positive numbers are 1 and 4.
Algebraic equation is nothing but a statement of the equality of two expressions formulated by applying algebraic operations to a set of variables, namely addition, subtraction, multiplication, division, raising to a power, and root extraction.
Let the 1st number be 'x' and 2nd number be 'y'
From given data,
we can express the equation as
[tex]xy=4\\\\y=\frac{4}{x}.....i[/tex]
Now,
again express the second data into expression
16x+4y
let
f(x)=16x+4y
substituting eq.i
[tex]f(x)=16x+4(\frac{4}{x})\\\\f(x)=16x+\frac{16}{x}[/tex]
We need to minimize the equation .i.e. we need to find the derivative of the equation by equating it to zero
[tex]f(x)=16x+\frac{16}{x}=0[/tex]
Applying derivative on both sides,
[tex]f'(x)=16-\frac{16}{x^2}=0\\\\16=\frac{16}{x^2}\\\\x^2=1\\\\x=\pm 1[/tex]
But we know that, the given number is positive then,
x=1
here, x=1 is also known as the critical value of the equation.
now, substitute 'x' value in eq.i, we get
(1)y=4
y=4
Hence, the two positive numbers are 1 and 4.
To learn more about algebraic equations refer here
https://brainly.com/question/29783039
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