2015 MTAP Reviewer for Grade 9 Solutions(16-20)
This is the 4th tutorial series about the solution to 2015 MTAP(MMC) elimination paper for grade 9. Links to other pages included here where you can enhance you knowledge in specific subject matter.
Solve for real numbers satisfying the inequality
Solving for x:
Obviously, -2 is an extraneous root since we have square root of x in the left side of equation and the square root of any number will always be greater than 0. Thus,
Check this tutorial on how to deal with quadratic inequality flawlessly.
Find the minimum value of
Minimum value of quadratic equation can be found using the following formula,
where a,b, and c are the coefficients of quadratic equation.
Find the smallest value of
By AM-GM Inequality theorem we have,
Applying the theorem,
Thus, the minimum value of x+5/x is
Solve for b in the equation:
By comparison, we can say that b=a+1. But a=3(constant part), hence
Write the quadratic equation with integer coefficients whose roots are the reciprocals of the roots of
Let y be the roots of the desired equation. Since the given equation has a root of x, we can establish the following relation based on the condition given(reciprocal of the roots).
Now, we substitute this to the given equation,
Simplifying to have an integer coefficients we have,
Dropping y back to x,