3 years ago

How do you use a abacus in a simple way?

1 answer:

7 0

Each column is a digit, and the top two beads each represent 5 and the bottom 5 beads each represent 1. To read it, you add up the values of the "top" beads that are dropped down and the "bottom" beads that are raised up, and you read the number left to right.

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3 years ago

Plz answer. What is the sum? 3x^2-2x-1/x-5 + -2x^2+x-5/x-5

IrinaVladis [17]

Answer:

Step-by-step explanation:

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vivado [14]

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Step-by-step explanation:

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3 years ago

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3 years ago

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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:

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

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3 years ago