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Running head: MATHEMATICS 1 Mathematics Question Name Institution MATHEMATICS 2 If x²+4y²=40 and xy=6, what will be the value of x+2y? Considering x and y as two positive real numbers. By utilizing algebraic identities, let us introduce a variable z and make the assumption that: z = (x + 2y)² Translating the above expression, we have; z = (x + 2y)(x + 2y) This expands to: z = x² + 4xy + 4y² Simplifying the expression, we have: z = (x² + 4y²) + 4xy z=(x² + 4y²) + 4(xy) By plugging in the values given: x²+4y²=40 and xy=6 z = 40 + 4*6 z = 40 + 24 z = 64 From our initial assumption of z = (x + 2y)², we have; z = (x + 2y)² = 64 By taking the square roots of both sides and considering both positive and negative values, we have: MATHEMATICS x + 2y = ±√64 x + 2y = ± 8 By considering x and y as positive real numbers, then: x+2y = 8 3 Name: Mathematics Question Descr ...
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