lilspike420

lilspike420

31.03.2021 •

Mathematics

The x-intercept of rufus third equation is blank and the y-intercept of rufus 3rd equation is blank

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Ответ:

asseatingbandit

09.08.2021

$x=i,\:x=-i,\:x=3i,\:x=-3i$

Step-by-step explanation:

0=x^4+10x^2+9

x^4+10x^2+9=0

u^2+10u+9=0 ; u=x^2, u^2=x^4

u^2+10u+9=0

Use quadratic equation:

$\frac{-10\pm \sqrt{10^2-4\cdot \:1\cdot \:9}}{2\cdot \:1}$

$\frac{-10+\sqrt{10^2-4\cdot \:1\cdot \:9}}{2\cdot \:1}$

$=\frac{-10+\sqrt{64}}{2\cdot \:1}$

$=\frac{-10+8}{2}$

$=-\frac{2}{2}$

$\frac{-10-\sqrt{10^2-4\cdot \:1\cdot \:9}}{2\cdot \:1}$

$\frac{-10-\sqrt{64}}{2\cdot \:1}$

$=\frac{-10-\sqrt{64}}{2}$

$=\frac{-18}{2}$

=-9

u=-1, u=-9

Substitute back in:

x^2=-1

$x=\sqrt{-1},\:x=-\sqrt{-1}$

$x=i,\:x=-i$

x^2=-9

$x=\sqrt{-9},\:x=-\sqrt{-9}$

$\sqrt{-9}=3i$ , $-\sqrt{-9}=-3i$

Therefore the solutions are:

$x=i,\:x=-i,\:x=3i,\:x=-3i$

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