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nata0808 [166]
3 years ago
9

Expand the following: 1/5 (10x-25)

Mathematics
1 answer:
mario62 [17]3 years ago
3 0
<span>This must be your answer:
Expanded: 1/5 x 10x + 1/5 x -25 </span>
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x^2+\dfrac1{x^2}=3\implies x^4+1=3x^2\implies x^4-3x^2+1=0

By the quadratic formula,

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(x^2+1)^2=\dfrac{25\pm10\sqrt5+5}4=\dfrac{15\pm5\sqrt5}2

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Multiply numerator and denominator by the denominator's conjugate:

\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}\cdot\dfrac{15\mp5\sqrt5}{15\mp5\sqrt5}=\dfrac{45\pm15\sqrt5\mp15\sqrt5-25}{15^2-(5\sqrt5)^2}=\dfrac{20}{100}=\dfrac15

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