Answer:
x= -3/5
Step-by-step explanation:
x+3=4x+8
-8 -x
-5 = 3x
-5/3 = x
Answer:
-3 sqrt 11
Step-by-step explanation:
The sqrt is the same so you just muliply the outside numbers normally.
19) x>4
20) k<7
21) y>1
22)x>13
23)n>8
24)x>44
25)b<14
26) s<3.5
27)m<1/4
28)x<2
29)n>7
30)x<5/3
31)b<3
32)p>2/5
33)k<3/11
<span><span> x3-81=0</span> </span>One solution was found : <span> x = 3 • ∛<span>3 </span>= 4.3267</span>
Step by step solution :<span>Step 1 :</span>Trying to factor as a Difference of Cubes:
<span> 1.1 </span> Factoring: <span> x3-81</span>
Theory : A difference of two perfect cubes, <span> <span>a3</span> - <span>b3</span> </span>can be factored into
<span> (a-b) • (a2 +ab +b2)</span>
Proof : <span> (a-b)•(a2+ab+b2) =
<span>a3</span>+<span>a2b</span>+<span>ab2</span>-<span>ba2</span>-<span>b2a</span>-<span>b3</span> =
<span>a3</span>+(<span>a2b</span>-<span>ba2</span>)+(<span>ab2</span>-<span>b2a</span>)-<span>b3</span> =
<span>a3</span>+0+0+<span>b3</span> =
<span>a3</span>+<span>b3</span></span>
<span>Check : 81 is not a cube !! </span>
Ruling : Binomial can not be factored as the difference of two perfect cubes
Polynomial Roots Calculator :
<span> 1.2 </span> Find roots (zeroes) of : <span> F(x) = x3-81</span>
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is <span> -81.
</span>The factor(s) are:
of the Leading Coefficient : <span> 1
</span>of the Trailing Constant : <span> 1 ,3 ,9 ,27 ,81
</span>Let us test ....
<span><span> P Q P/Q F(P/Q) Divisor</span><span> -1 1 -1.00 -82.00 </span><span> -3 1 -3.00 -108.00 </span><span> -9 1 -9.00 -810.00 </span><span> -27 1 -27.00 -19764.00 </span><span> -81 1 -81.00 -531522.00 </span><span> 1 1 1.00 -80.00 </span><span> 3 1 3.00 -54.00 </span><span> 9 1 9.00 648.00 </span><span> 27 1 27.00 19602.00 </span><span> 81 1 81.00 531360.00 </span></span>
Polynomial Roots Calculator found no rational roots
<span>Equation at the end of step 1 :</span><span> x3 - 81 = 0
</span><span>Step 2 :</span>Solving a Single Variable Equation :
<span> 2.1 </span> Solve : <span> x3-81 = 0</span><span>
</span>Add 81 to both sides of the equation :<span>
</span> <span> x3 = 81</span>
When two things are equal, their cube roots are equal. Taking the cube root of the two sides of the equation we get: <span>
</span> x = <span> ∛<span> 81 </span></span><span>
</span>Can <span> ∛<span> 81 </span></span>be simplified ?
Yes! The prime factorization of 81 is
<span> 3•3•3•3</span>
To be able to remove something from under the radical, there have to be <span> 3 </span> instances of it (because we are taking a cube i.e.<span> cube </span>root).
<span>∛<span> 81 </span> = ∛<span> 3•3•3•3 </span> =
<span>3 </span>• ∛<span> 3 </span></span>
The equation has one real solution
This solution is <span> x = 3 • ∛<span>3 </span>= 4.3267 </span>
One solution was found : <span> x = 3 • ∛<span>3 </span>= 4.3267</span>
Answer:
-1, 0, 2
Step-by-step explanation:
Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)
