Apoorvisb
Select for a and for b values such that the equation X/a = x − b has more than one solution for x. Make only two selections, one in each column.
can anyone solve?
Here two methods:
1. Algebra
2. Visual
Using algebra you need a 2nd degree equation
so
x = ax - ba
multiply by x
x^2 = a*x^2 + b*a*x
then
0 = a*x^2 - x^2 + b*a*x
x(a*x-x+ab) = 0
Then one solution is 0
the other
x(a-1) + ab = 0
x = a*b / (1 -a )
if you substitute
x = ax - ba
x (a-1) = b*a
x = b*a /(a-1)
As we know that one solution of x is 0 we can substitute
0 = b*a
so one of the two should be 0, lets put b, so then
x(a-1) = 0
x => is 0
so
a = 1
let's try
1/1 = x -1
x = 2
0/1 = 0 - 0 => 0
2/1 = 2 - 0 => 2
so we have the answer
a*b / (1 -a ) = a*( a*b / (1 -a ) - b)
you can remove a from the top
b/(1-a) = ab/(1-a) - b(1-a)/(1-a)
now (1-a) from the bottom
b = ab -b + ab
2. Visual
x/a = is the equation of a line
x-b is the equation of the other line
how two lines could have more than one solution:
Parallel - 0
Perpendicular - 1
same line - infinity
so we need that both are the same line
y = x/a
y = x - b
remember a lines is y = mx + b -> where m is the slope and b is the cut in Y
so on the first equation b is 0 -> so **b=0**
and the slope on the second is 1 -> so **a=1**