Find the real and complex solutions of x^4+12x^2=-27

Question

asked Jun 7, 2023 143k views

1 Answer

Nneka · Answer 1 · 2023-06-14T04:33:31+0000

Answer:

$x=\pm√(3i) ,\pm3i$

Explanation:

1) Move all terms to one side.

${x}^(4)+12{x}^(2)+27=0$

2) Factor
${x}^(4)+12{x}^(2)+27x$ .

1) Ask: Which two numbers add up to 12nd multiply to 27?

3 and 9

2) Rewrite the expression using the above.

$({x}^(2)+3)({x}^(2)+9)$

Outcome:
$({x}^(2)+3)({x}^(2)+9)=0$

2) Solve for x.

1)Ask: When will
$({x}^(2)+3)({x}^(2)+9)$ equal zero?

When
${x}^(2)+3=0$ or
${x}^(2)+9=0$

2) Solve each of the 2 equations above.

$x=\pm√(3i) ,\pm3i$

Thanks.