All categories

2 years ago

Solve each equation by finding all roots x^4-16=0

Mathematics

2 answers:

Alexandra [31]2 years ago

4 0

Add both sides by 16
so you'll have x^4 =16
take the 4th root of both sides and you'll get x= 2

SashulF [63]2 years ago

3 0

${ x }^{ 4 }-16=0\\ \\ { x }^{ 4 }=16\\ \\ x=\pm \sqrt [ 4 ]{ 16 } \\ \\ \therefore \quad x=\pm 2$

You might be interested in

Find the perimeter and area of the polygon with E(0, 0), F(7, 0), G(7, 2), H(0, 2)

pav-90 [236]

i think not sure sorry if i got it wrong but ya

4 0

2 years ago

Read 2 more answers

Please see picture below, it has the question

Galina-37 [17]

Answer:

the qmswrt would be b

Step-by-step explanation:

I thijk

5 0

3 years ago

Read 2 more answers

Let a and b be roots of x² - 4x + 2 = 0. find the value of a/b² +b/a²

erastovalidia [21]

Answer:

$\dfrac{a}{b^2}+\dfrac{b}{a^2}=10$

Step-by-step explanation:

Given equation: $x^2-4x+2=0$

The roots of the given quadratic equation are the values of x when $y=0$ .

To find the roots, use the quadratic formula:

$x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0$

Therefore:

$a=1, \quad b=-4, \quad c=2$

$\begin{aligned}\implies x & =\dfrac{-(-4) \pm \sqrt{(-4)^2-4(1)(2)}}{2(1)}\\& =\dfrac{4 \pm \sqrt{8}}{2}\\& =\dfrac{4 \pm 2\sqrt{2}}{2}\\& =2 \pm \sqrt{2}\end{aligned}$

$\textsf{Let }a=2+\sqrt{2}$

$\textsf{Let }b=2-\sqrt{2}$

Therefore:

$\begin{aligned}\implies \dfrac{a}{b^2}+\dfrac{b}{a^2} & = \dfrac{2+\sqrt{2}}{(2-\sqrt{2})^2}+\dfrac{2-\sqrt{2}}{(2+\sqrt{2})^2}\\\\& = \dfrac{2+\sqrt{2}}{6-4\sqrt{2}}+\dfrac{2-\sqrt{2}}{6+4\sqrt{2}}\\\\& = \dfrac{(2+\sqrt{2})(6+4\sqrt{2})+(2-\sqrt{2})(6-4\sqrt{2})}{(6-4\sqrt{2})(6+4\sqrt{2})}\\\\& = \dfrac{12+8\sqrt{2}+6\sqrt{2}+8+12-8\sqrt{2}-6\sqrt{2}+8}{36+24\sqrt{2}-24\sqrt{2}-32}\\\\& = \dfrac{40}{4}\\\\& = 10\end{aligned}$

6 0

1 year ago

Read 2 more answers

Beth is 2 years older than Jimmy, and in 3 years the sum of their ages will be twice as much as the sum of their ages 3 years ag

Alika [10]

Jimmy is 8
Beth is 10

8 0

3 years ago

A dog weighs 2 pounds less than 3 times the weight of a cat. The dog weighs twenty two more pounds than the cat

Nesterboy [21]

Complete Question

A dog weighs 2 pounds less than 3 times the weight of a cat. The dog weighs twenty two more pounds than the cat.

Write and solve an equation to find the weights of the cat and the dog.

Answer:

Weight of cat = x = 12 pounds

Weight of Dog = y = 34 pounds

Step-by-step explanation:

Let's represent:

Weight of cat = x

Weight of Dog = y

A dog weighs 2 pounds less than 3 times the weight of a cat.

y = 3x - 2........ Equation 1

The dog weighs twenty two more pounds than the cat

y = x + 22....... Equation 2

The equation is given as:

y = y

3x - 2 = x + 22

Collect like terms

3x - x = 22 + 2

2x = 24

x = 24/2

x = 12 pounds

Solving for y using any of the equations:

y = 3x - 2

y = 3 × 12 - 2

y = 36 - 2

y = 34 pounds

Therefore:

Weight of cat = x = 12 pounds

Weight of Dog = y = 34 pounds

6 0

2 years ago