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How do you use u-substitution, solve for all the real value(s) of 'x' for the equation #x^4-3x^2=10#?

Answer 1

Scarlett Allison

I am not sure if I got the idea of the question right but anyway:

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Answer 2

Emily Ammerman

To solve the equation (x^4 - 3x^2 = 10) using u-substitution:

Let (u = x^2).
Substitute (u) into the equation: (u^2 - 3u = 10).
Rearrange the equation to form a quadratic equation: (u^2 - 3u - 10 = 0).
Factor the quadratic equation: ((u - 5)(u + 2) = 0).
Solve for (u): (u = 5) or (u = -2).
Substitute back (x^2) for (u) and solve for (x):
- When (u = 5), (x^2 = 5), so (x = \sqrt{5}) or (x = -\sqrt{5}).
- When (u = -2), (x^2 = -2), but there are no real solutions for (x) since the square of a real number cannot be negative.

Therefore, the real solutions for (x) are (x = \sqrt{5}) and (x = -\sqrt{5}).

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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.