Find roots of equation $\displaystyle { a }^{ 4 }{ x }^{ 2 }-{ b }^{ 4 }=0$
- $\displaystyle { { b }^{ 2 } }/{ { a }^{ 2 } },-{ { b }^{ 2 } }/{ { a }^{ 2 } }$
- $\displaystyle { { b }^{ 2 } }/{ { a }^{ 2 } },{ { b }^{ 2 } }/{ { a }^{ 2 } }$
- $\displaystyle { { a }^{ 2 } }/{ { { b }^{ 2 } } },\frac { { a }^{ 2 } }{ { { b }^{ 2 } } } $
- $\displaystyle { { a }^{ 2 } }/{ { { b }^{ 2 } } },-\frac { { a }^{ 2 } }{ { { b }^{ 2 } } } $
Reveal answer
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A
Correct answer
Explanation
a^4 * x^2 = b^4 implies x^2 = b^4 / a^4. Taking the square root gives x = +/- b^2 / a^2.
AI explanation
Using the difference of squares formula, factor the equation as (a^2x + b^2)(a^2x - b^2) = 0. Setting each factor to zero gives a^2x = -b^2 and a^2x = b^2. Solving these yields x = -b^2/a^2 and x = b^2/a^2, so the roots are b^2/a^2 and -b^2/a^2.