Problem preview

A-CED.4 Warmup M3-011-A02-V04

Rearrange formulas to highlight a chosen quantity across the expression types studied.

Isolate a powered variable with explicit real branches and conditions

Problem

In \(K~=~2x^4\), isolate all real \(x\). State the real condition on \(K\) and include all branches.

Answer choices

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x=±⁴√(K/2) for every real K.

x=±⁴√(K/2), provided K≥0, because both real fourth-root branches are needed.

x=K/8 for every real K.

x=⁴√(K/2), provided K≥0, using only the positive branch.

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Curriculum context

Course: Math III
Standard: A-CED.4
Category: Algebra
Domain: Creating Equations
Objective: Rearrange formulas to highlight a chosen quantity across the expression types studied.
Problem type: Isolate a powered variable with explicit real branches and conditions