3 years ago

Find the value of x with explanation please

Mathematics

1 answer:

zmey [24]3 years ago

8 0

Answer:

11.2

Step-by-step explanation:

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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

State a true conclusion.

FromTheMoon [43]

Answer:

RQ + QS = RS

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3 years ago

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Ludmilka [50]

Answer:

<h2>The first one is the answer</h2>

Step-by-step explanation:

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2 years ago

8x = -6 please answer!!

Nikolay [14]

Answer:-3/4

Step-by-step explanation:

Get the x by itself by dividing both sides by 8 then reduce -6/8. When you reduce you get -3/4

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4 years ago

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Answer:

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Step-by-step explanation:

No seresly is that the question

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