If x3 + x5 = 1615, find the rational number x.

Step-by-step solution

Idea: Combine the two fractions over the common denominator 15, then compare numerators.

1. x3 + x5 = 5x15 + 3x15 = 8x15.1 mark
2. 8x15 = 1615 gives 8x = 16, so x = 2.1 mark

Check: 23 + 25 = 1015 + 615 = 1615 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Adding the denominators: x3 + x5 = 2x8.
• Getting 8x = 16 and writing x = 8 or x = 128.
• Writing x3 = 3x15 (should be 5x15).

How this can come in the exam

Try one yourself

Find x if x2 + x7 = 2714.

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