book Maths Puzzle Numerical Ability

Write a system of two equations in two unknown. Solved by method of choice. I can't figure out how to pull out the data and set it up.

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book Other Question

Use parabolas to work the following problem: find two numbers having a sum of 50 such that the sum of the square of one and three times the square of the other is a minimum. Can you explain how to substitute cot (angle) with 1/root3