## Grade 9 MTAP 2015 Elimination Questions with Solutions – Part 2

This is the second part (questions 11-20) of the solutions of the Grade 9 MTAP 2015 Elimination Questions. The first part can be read here.

Although reasonable care has been given to make the solution accurate as possible, the solver is also human. Please comment below if you see any errors.

11.) If $x \neq 1$, solve for $x$ in $2 \sqrt{x} + \frac{3}{\sqrt{x}} = 5$.

Solution
Multiplying both sides by $\sqrt{x}$, we obtain

$2x + 3 = 5\sqrt{x}$

Squaring both sides of the equation, we get

$4x^2 + 12x + 9 = 25x$

$4x^2 - 13x + 9 = 0$.

Factoring, we have

$(4x - 9)(x - 1) = 0$

So, $x = \frac{9}{4}$ or $x = 1$.

But from the given above, $x \neq 1$, so the only solution is $x = \frac{9}{4}$

## 2015 Grade 9 MTAP Math Challenge – Division Orals

Below are the 2015 Grade 9 MTAP Math Challenge Division Oral Competition questions with answers.

15-second question (2 points each)

1.) Determine all positive number x that satisfy $5x^2 = 10x$.
2.) What is the fourth power of $\sqrt{2 + \sqrt{2}}$?
Answer: $6 + 4 \sqrt{2}$
3.) Simplify $4^{\frac{-k}{2}} + 8^ {- \frac{k-1}{3}}$
Answer: $\frac{3}{2}^k$
4.) If a ♠ b = $\sqrt{a^2+b^2}$, what is the value of (3 ♠ 4) ♠ 12?