3 years ago

6. Nicole deposits $2,136 in a såvings account paying 5% interest rate. To the

Mathematics

1 answer:

ValentinkaMS [17]3 years ago

8 0

Answer: $3,166

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 Express answer as a common fraction. 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

What is 7 times the sum of a squared and b minus 4 times the sum of a squared and b

spayn [35]

The sum of a squared and b is given by
$a^2+b$

7 times the sum of a squared and b is given by
 $7(a^2+b)$
while 4 times the sum of a squared and b is given by
 $4(a^2+b)$

Therefore, 7 times the sum of a squared and b minus 4 times the sum of a squared and b is given by

$7(a^2+b)-4(a^2+b)=3(a^2+b)$