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Fiesta28 [93]
3 years ago
15

Equation equivalent to 5x(3x+4)

Mathematics
2 answers:
Vika [28.1K]3 years ago
7 0

use the distributive property

5x(3x+4)

15x^2 +20x

defon3 years ago
4 0
Using distributive property, we can find that
15X^2+20X is the same as 5X(3X+4)
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1/12piX^3

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If x^2+1/x^2=3 find the value of x^2/(x^2+1)^2<br> Express answer as a common fraction.<br> Thanks!!
timama [110]

x^2+\dfrac1{x^2}=3\implies x^4+1=3x^2\implies x^4-3x^2+1=0

By the quadratic formula,

x^2=\dfrac{3\pm\sqrt5}2\implies x^2+1=\dfrac{5\pm\sqrt5}2

Then

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

\implies\dfrac{x^2}{(x^2+1)^2}=\dfrac{\frac{3\pm\sqrt5}2}{\frac{15\pm5\sqrt5}2}=\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}

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

3 0
3 years ago
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