Find the roots of ax2 +a = a2x+x
Answers
Answer:
the roots of the equation ax² - x(a² + 1) + a =0 are 'a' and '1/a'
Step-by-step explanation:
our goal is to find the roots of the equation:
ax² + a = a²x + x
rearrange the above equation:
ax² - a²x - x + a =0
take 'x' common from 2nd and 3rd terms of above equation;
ax² - x(a² + 1) + a =0
it is a simple quadratic equation.
it can also be written as;
ax(x - a) - 1( x - a) = 0 by taking common from first and last two terms of the equation : ax² - a²x - x + a =0
finally , it becomes :
(ax - 1)(x - a) = 0
x = a or x = 1/a
the roots of the equation ax² - x(a² + 1) + a =0 are 'a' and '1/a'
Answer:
The roots of the equation ax² - x(a² + 1) + a =0 are 'a' and '1/a'
Step-by-step explanation:
- In context to the given question we have to find the roots of the given equation
Given equation;
ax² + a = a²x + x
By transposing method , we get
ax² - a²x - x + a =0
By further simplifying it by removing common "x" we get;
ax² - x(a² + 1) + a =0
Now, it is in the form of quadratic equation
Further, by solving the quadratic equation we get;
ax (x - a) - 1( x - a) = 0
(ax - 1)(x - a) = 0
x = a or x = 1/a
- Therefore the roots of the equation ax² - x(a² + 1) + a =0 are 'a' and '1/a'