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yaroslaw [1]
3 years ago
11

X^3+216=0 solve the equation , try your solutions

Mathematics
2 answers:
Veronika [31]3 years ago
5 0
X³  + 216 = 0

x³   = 0 - 216

x³   = - 216    Take the cube root of both sides.

∛x³ =  ∛-216

x = -6


Check:

x³  + 216 = 0,    x = -6

(-6)³  + 216 = 0

-216 + 216 = 0

0  =  0          Correct.
Gnom [1K]3 years ago
5 0
 
<span>  x = -6 </span>

Factoring: <span> x3+216</span>   

A sum of two perfect cubes, <span> <span>a3</span> + <span>b3</span></span> can be factored in to: (a+b) • (a2-ab+b2)


Proof  : (a+b) • (a2-ab+b2) =
<span>    <span>a3</span>-<span>a2b</span>+<span>ab2</span>+<span>ba2</span>-<span>b2a</span>+<span>b3</span> =</span>
<span>    <span>a3</span>+(<span>a2b</span>-<span>ba2</span>)+(<span>ab2</span>-<span>b2a</span>)+<span>b3</span>=</span>
<span>    <span>a3</span>+0+0+<span>b3</span>=</span>

<span>    <span>a3</span>+<span>b3</span></span>

Check :  216  is the cube of   6

<span>Factorization is :
</span>            <span> (x - 6)  • </span><span> (x^2 + 6x + 36)</span>

Hope This Helped


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