Asked by bob
𝑥^6 −15 =5𝑥^4 −𝑥^2 solve by graphing, list solutions from least to greatest
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GPT-5 mini
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Solve x^6 − 15 = 5x^4 − x^2
Rearrange: x^6 − 5x^4 + x^2 − 15 = 0.
Let t = x^2 (t ≥ 0). Then
t^3 − 5t^2 + t − 15 = 0.
This cubic has one real root t ≈ 5.33896, so x = ±√t ≈ ±2.31062.
Listed least to greatest:
x ≈ −2.311, 2.311
Rearrange: x^6 − 5x^4 + x^2 − 15 = 0.
Let t = x^2 (t ≥ 0). Then
t^3 − 5t^2 + t − 15 = 0.
This cubic has one real root t ≈ 5.33896, so x = ±√t ≈ ±2.31062.
Listed least to greatest:
x ≈ −2.311, 2.311
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