WAEC 2017 Mathematics · Question 31

Make x the subject of the relation d = $\sqrt{\frac{6}{x} - \frac{y}{2}}$

Options

A.x = $\frac{6 + 12}{d^2 + y}$
B.x = $\frac{12}{d^2 - y}$
C.x = $\frac{12}{y} - 2d^2$
D.x = $\frac{12}{2d^2 + y}$

Answer: D. x = $\frac{12}{2d^2 + y}$

Explanation written with AI and checked against the answer key

Step 1: Analyze the question We need to isolate x in d = √(6/x − y/2). Step 2: Concept Remove the square root by squaring both sides, then collect the x term and rearrange. Step 3: Solution Square both sides: d² = 6/x − y/2 Add y/2 to both sides: d² + y/2 = 6/x Combine the left side over a common denominator: (2d² + y)/2 = 6/x Cross-multiply: x(2d² + y) = 12 Divide: x = 12 / (2d² + y) Step 4: Identify the answer This matches option D. Options A, B and C do not match. For example, B would require d² − y with no factor of 2, which is wrong because the y/2 sign and the common denominator both matter. Tip: When x is stuck in a fraction inside a root, square first, then get the x-term alone, and cross-multiply. Watch out for fractions like y/2. Multiply the whole equation by the denominator (here 2) so you don't lose factors.

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Make x the subject of the relation d = 6x−y2\sqrt{\frac{6}{x} - \frac{y}{2}}x6​−2y​​

Options

Answer: D. x = 122d2+y\frac{12}{2d^2 + y}2d2+y12​

Make x the subject of the relation d = $\sqrt{\frac{6}{x} - \frac{y}{2}}$

Answer: D. x = $\frac{12}{2d^2 + y}$