: Setting up the equation as x + 1/x = 10/3 creates a quadratic form 3x square – 10x + 3 = 0. Factoring this gives (3x – 1)(x – 3) = 0, which provides the two possible numerical answers.
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A polynomial of degree 1 can be 3x plus 2. A polynomial of degree 2 can be x square plus 5x plus 1. A polynomial of degree 3 can be 2x cube minus x plus 4.
If the length of the rectangle is x cm, then the width becomes 10 minus x cm because the total perimeter is 20 cm. Therefore, the area of the rectangle is x multiplied by 10 minus x.
The total cost of decorating the garden is found by adding fencing and seed costs. Wire fencing costs 200l rupees, wooden fencing costs 160w rupees and seeds cost 50lw rupees. Therefore, total cost equals 200l + 160w + 50lw.
The algebraic expression in Example 1 has separate variables x and y in different terms. But in Example 2, the term 50lw contains two variables multiplied together. Example 2 also represents cost using area and fencing calculations.