A Nice Algebra Math Simplification | Math Olympiad
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- Опубликовано: 16 май 2024
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Check out this video on how to solve for a in this nice algebra Math Simplification, Math Olympiad
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√3a=a^2 則3a=a^4 3=a^3
a=3^(1/3)
a² / √3 = √a
(a² / √3)² = a
a⁴ / 3 = a
3(a⁴ / 3) = (a)3
a⁴ = 3a
a⁴/a = 3
a^(4 - 1) = 3
a³ = 3
a = ³√3
asnwer=1x isit
Math Olympiad: a²/√3 = √a; a = ?
a ≥ 0; (a²/√3)² = (√a)², a⁴ = 3a, a⁴ - 3a = a[a³ - (³√3)³] = 0
a(a - ³√3)[a² + a(³√3) + (³√3)²] = 0, a ≥ 0; a² + a(³√3) + (³√3)² > 0
a = 0 or a - ³√3 = 0; a = ³√3
Answer check:
a = 0: a²/√3 = 0/√3 = 0 = √a; Confirmed
a = ³√3: a²/√3 = (³√3)²/√3 = 3⁽²⸍³⁻¹⸍²⁾ = 3¹⸍⁶ = ⁶√3,
√a = √(³√3) = (3¹⸍³)¹⸍² = 3¹⸍⁶ = ⁶√3; Confirmed
Final answer:
a = 0 or a = ³√3
[(a^2)÷/3]=/a : [(a^4)/3]=a :a^4=3a : a=4/3a