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Running head: Mathematics Question 1 Mathematics Question Student Name: Instructor Name: Course: Date: Mathematics Question 2 1. If x²+4y²=40 and xy=6, what will be the value of x+2y? Please explain how you arrived at your answer. Solutions If x²+4y²=40 and xy=6, what will be the value of x+2y? Let's Z be: z = (x + 2y)² Expanding the values, z = (x + 2y)(x + 2y) z = x² + 4xy + 4y² Collecting like terms together as follows: z = (x² + 4y²) + 4(xy) Substitute in the values you were given and you have: z = 40 + 4*6 z = 40 + 24 z = 64 then we equate with: z = (x + 2y)² = 64 Taking the square root of both sides, recalling there are two possible roots (positive and negative): x + 2y = ±√64 x + 2y = ± 8 but x and y as positive real numbers, this means thatwe can ignore the negative value. Hence our Answer will be: 8 Mathematics Question 3 Reference 1. Tang, X., Lin, X., ...
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