1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Soloha48 [4]
3 years ago
6

How would I solve 16x^4-41x^2+25=0 ???

Mathematics
2 answers:
hichkok12 [17]3 years ago
8 0
16x⁴ - 41x² + 25 = 0
16x⁴ - 16x² - 25x² + 25 = 0
16x²(x²) - 16x²(1) - 25(x²) + 25(1) = 0
16(x² - 1) - 25(x² - 1) = 0
(16x² - 25)(x² - 1) = 0
(16x² + 20x - 20x - 25)(x² - x + x - 1) = 0
(4x(4x) + 4x(5) - 5(4x) - 5(5))(x(x) - x(1) + 1(x) - 1(1)) = 0
(4x(4x + 5) - 5(4x + 5))(x(x - 1) + 1(x - 1)) = 0
(4x - 5)(4x + 5)(x + 1)(x - 1) = 0
4x - 5 = 0  or  4x + 5 = 0  or  x + 1 = 0  or  x - 1 = 0
<u>    + 5 + 5</u>       <u>      - 5  - 5</u>      <u>    - 1  - 1</u>       <u>   + 1 + 1</u>
     <u>4x</u> = <u>5</u>              <u>4x</u> = <u>-5</u>          x = -1             x = 1
      4     4               4      4
       x = 1¹/₄            x = -1¹/₄

The solution set is equal to {(1¹/₄, -1¹/₄, -1, 1)}.
sveticcg [70]3 years ago
3 0
16{ x }^{ 4 }-41{ x }^{ 2 }+25=0

{ x }^{ 4 }={ ({ x }^{ 2 }) }^{ 2 }\\ \\ 16{ ({ x }^{ 2 }) }^{ 2 }-41{ x }^{ 2 }+25=0



First of all to make our equation simpler, we'll equal x^{2} to a variable like 'a'.

So,

{ x }^{ 2 }=a

Now let's plug x^{2} 's value (a) into the equation.

16{ ({ x }^{ 2 }) }^{ 2 }-41{ x }^{ 2 }+25=0\\ \\ { x }^{ 2 }=a\\ \\ 16{ (a) }^{ 2 }-41{ a }+25=0

Now we turned our equation into a quadratic equation.

(The variable 'a' will have a solution set of two solutions, but 'x' , which is the variable of our first equation will have a solution set of four solutions since it is a quartic equation (<span>fourth-degree <span>equation) )

Let's solve for a.

The formula used to solve quadratic equations ;

\frac { -b\pm \sqrt { { b }^{ 2 }-4\cdot t\cdot c }  }{ 2\cdot t }

The formula is used in an equation formed like this :
</span></span>
t{ x }^{ 2 }+bx+c=0

In our equation,

t=16 , b=-41 and c=25

Let's plug the values in the formula to solve.

t=16\quad b=-41\quad c=25\\ \\ \frac { -(-41)\pm \sqrt { -(41)^{ 2 }-4\cdot 16\cdot 25 }  }{ 2\cdot 16 } \\ \\ \frac { 41\pm \sqrt { 1681-1600 }  }{ 32 } \\ \\ \frac { 41\pm \sqrt { 81 }  }{ 32 } \\ \\ \frac { 41\pm 9 }{ 32 }

So the solution set :

\frac { 41+9 }{ 32 } =\frac { 50 }{ 32 } \\ \\ \frac { 41-9 }{ 32 } =\frac { 32 }{ 32 } =1\\ \\ a\quad =\quad \left\{ \frac { 50 }{ 32 } ,\quad 1 \right\}

We found a's value.

Remember,

{ x }^{ 2 }=a

So after we found a's solution set, that means.

{ x }^{ 2 }=\frac { 50 }{ 32 }

and

{ x }^{ 2 }=1

We'll also solve this equations to find x's solution set :)

{ x }^{ 2 }=\frac { 50 }{ 32 } \\ \\ \frac { 50 }{ 32 } =\frac { 25 }{ 16 } \\ \\ { x }^{ 2 }=\frac { 25 }{ 16 } \\ \\ \sqrt { { x }^{ 2 } } =\sqrt { \frac { 25 }{ 16 }  } \\ \\ x=\quad \pm \frac { 5 }{ 4 }

{ x }^{ 2 }=1\\ \\ \sqrt { { x }^{ 2 } } =\sqrt { 1 } \\ \\ x=\quad \pm 1

So the values x has are :

\frac { 5 }{ 4 } , -\frac { 5 }{ 4 } , 1 and -1

Solution set :

x=\quad \left\{ \frac { 5 }{ 4 } \quad ,\quad -\frac { 5 }{ 4 } \quad ,\quad 1\quad ,\quad -1 \right\}

I hope this was clear enough. If not please ask :)



You might be interested in
Walking at a constant rate of 8 kilometers per hour, juan can cross a bridge in 6 minutes. What is the length of the bridge in m
Mama L [17]

Answer:

800 m

Step-by-step explanation:

1 km = 1,000 m

8 km = 8,000 m

1 hour = 60 minutes

6 minutes is 1/10 of an hour

1/10 of 8,000 m = 800 m

Answer: 800 m

7 0
3 years ago
Select the correct answer.
Vedmedyk [2.9K]

Answer:

Addition.

Step-by-step explanation:

Addition was used to add 5 to both sides, leaving x by itself.

7 0
3 years ago
If you had $9 what would you buy
Karolina [17]

Answer:

Food

Step-by-step explanation:

You need food to survive so find some good food and eat it :)

4 0
2 years ago
Read 2 more answers
Hey i just wanted to try typing a question so whats 2+2?​
zloy xaker [14]

ummm...... 4 hahahahaha

7 0
2 years ago
How are &lt;8 and &lt;4 related
Tasya [4]

Answer:

8 divided by 2 is 4

Step-by-step explanation:

U divide 8 from 2

3 0
3 years ago
Other questions:
  • Which algebraic expression represents the phrase “the quotient of negative eight and the sum of a number and three”?
    7·1 answer
  • What is the answer to the question
    9·1 answer
  • A truck travels at the rate of 80 kilometers per hour. how much distance will it travel in 30 minutes?
    7·1 answer
  • Can someone help me with geometry! PLEASE!
    13·1 answer
  • Please help me with this question I don’t know how to do it. PLEASE!!!!!!!!!
    10·2 answers
  • Evaluate the expression.<br> m = 0.3 for m = 1.8
    9·1 answer
  • Find the measure of x.
    5·1 answer
  • 1+log2=log(x+1)<br><br> I know that x=19 but how do you get 19?
    5·1 answer
  • The lines (m-2)x+y=2 and mx+2y=k intersect at (2,8). Find the values of m and k
    9·1 answer
  • Find the missing angle measure in each triangle as acute, right or obtuse
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!