Question 540359
The two numbers can be defined as:
x
x+1
.
so their reciprocals are:
1/x
1/(x+1)
.
1/x + 1/(x+1) = 16/15
.
((x+1)+x)/(x*(x+1) = 16/15
.
15((x+1)+x) = 16(x*(x+1))
.
15x + 15 + 15x = 16(x^2 +x)
.
30x + 15 = 16x^2 +16x
.
0 = 16x^2 -14x -15
.
16x^2 -14x -15 = 0
.
(16x+10)(x-3/2) = 0
.
Check with FOIL.
16x^2 -24x +10x -15
Correct
.
So, x = -5/8 or x=3/2
.
{{{ graph(500,500,-5,5,-20,20,16*x^2-14*x-15) }}}
.
Or you could solve with quadratic equation.
.
*[invoke quadratic "x", 16, -14, -15 ]