How do you solve the quadratic #3+1/x=10/x^2# using any method?

Answer 1

#x= -2# or #+5/3#

#3+1/x=10/x^2#
Multiply through by #x^2 -> 3x^2+x=10#
#3x^2+x-10=0#
#(x+2)(3x-5)=0#
#x=#either #-2# or #+5/3#
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Answer 2

To solve the quadratic equation 3 + 1/x = 10/x^2, you can follow these steps:

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

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

  3. Use the quadratic formula to solve for x: x = (-b ± √(b^2 - 4ac)) / (2a)

    where a = 3, b = 1, and c = -10.

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

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

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

  7. 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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Answer from HIX Tutor

When evaluating a one-sided 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 one-sided 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 one-sided 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 one-sided 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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