The solution to the equation 1/x =x+3/2x^2 is x = 0 and 3. Option C
How to determine the equation
In solving for the values of 'x' we need to:
- Simplify the expression, that is, make a quadratic equation
- Solve the quadratic equation formed by either fractorisation or completing the square methods
Given the expression;
1/x =x+3/2x^2
Cross multiply
x ( x+ 3) = 2x² ( 1)
Expand the bracket
x² + 3x = 2x²
collect like terms and equate all the variables to zero, we have ;
2x² - x² - 3x = 0
We then subtract the like terms, we getv
x²- 3x = 0
Now, let's find the common factor
Factor out 'x':
x ( x - 3 ) = 0
Equate each of the factors to zero and find the value of 'x' for each
So,
x = 0
And
x - 3 = 0
x = 3
Thus, the solution to the equation 1/x =x+3/2x^2 is x = 0 and 3. Option C
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