How do you solve the quadratic #3+1/x=10/x^2# using any method?
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To solve the quadratic equation 3 + 1/x = 10/x^2, you can follow these steps:

Rewrite the equation with a common denominator: 3x^2 + x = 10

Rearrange the terms to form a quadratic equation in standard form: 3x^2 + x  10 = 0

Use the quadratic formula to solve for x: x = (b ± √(b^2  4ac)) / (2a)
where a = 3, b = 1, and c = 10.

Substitute the values of a, b, and c into the quadratic formula: x = ((1) ± √((1)^2  4(3)(10))) / (2(3))

Simplify the expression under the square root: x = (1 ± √(1 + 120)) / 6

Further simplify: x = (1 ± √121) / 6 x = (1 ± 11) / 6

Solve for both possible values of x: x1 = (1 + 11) / 6 = 10 / 6 = 5/3 x2 = (1  11) / 6 = 12 / 6 = 2
Therefore, the solutions for the quadratic equation 3 + 1/x = 10/x^2 are x = 5/3 and x = 2.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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