Solve this equation and show your work! (1 point for the correct answer and 1 point for showing how to solve the equation) x³ = -2,197

Question

asked Feb 3, 2021 222k views

2 Answers

Shanqn · Answer 1 · 2021-02-08T04:31:50+0000

Here we are given with a equation:

${x}^(3) = - 2197$

And we have to solve it with appropriate steps.

So, let's start solving.

Add 2197 to both sides of the equation,

${x}^(3) + 2197 = - 2197 + 2197$

${x}^( 3) + 2197 = 0$

Now, using the identity:

Let's proceed further.

x³ is the cube of x and 2197 is the cube of 13

$(x) {}^(3) + (13) {}^(3) = 0$

$(x + 13)( {x}^(2) - x * 13 + {13}^(2) ) = 0$

$(x + 13)( {x}^(2) - 13x + 13) = 0$

Now,

So, x = -13

And, for the second let's use the discriminate formula,

➝ D = b² - 4ac

➝ D = (-13)² - 4(1)(13)

➝ D = 169 - 52

➝ D = 117

Now, using the D. formula,

$x = ( - b \pm √( D) )/(2a)$

$x = (13 \pm √(117) )/(2)$

$x = (13 \pm 3 √(13) )/(2)$

So the roots of the equation are:

${ \boxed{ \bf{x = - 1 ,\: (13 + 3 √(13) )/(2) and \: (13 - 3 √(13) )/(2) }}}$

And we are done !!

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