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3 years ago

The inequality to model the situation is:

Mathematics

1 answer:

Bogdan [553]3 years ago

7 0

Answer:

Greater than or equal to

Step-by-step explanation:

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Factor over complex numbers 2x^4+36x^2+162

Darina [25.2K]

<u>Answer:</u>

Factor over complex numbers of $2 x^{4}+36 x^{2}+162$ is $2(x+3 i)^{2}(x-3 i)^{2}$

<u>Solution: </u>

From question given that

$2 x^{4}+36 x^{2}+162$ → (1)

On substituting $x^{2}=y$ in equation (1),

$=2 y^{2}+36 y+162$

Taking 2 as a common in above expression,

$=2\left(y^{2}+18 y+81\right)$

Rewrite the above expression,

$=2\left[y^{2}+2(y)(9)+9^{2}\right]$

$=2(y+9)^{2}$ $\left[\text { Using }(a+b)^{2}=a^{2}+2 a b+b^{2}\right]$

$=2\left(x^{2}+9\right)^{2}$ $\left[\text { since } y=x^{2}\right]$

$\left[\text { Using } a^{2}+b^{2}=(a+i b)(a-i b), \text { where } i=\sqrt{-1}\right]$

$=2[(x+3 i)(x-3 i)]^{2}$

$=2(x+3 i)^{2}(x-3 i)^{2}$

Hence Factor over complex numbers of $2 x^{4}+36 x^{2}+162$ is $2(x+3 i)^{2}(x-3 i)^{2}$

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4 years ago

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Pani-rosa [81]

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Step-by-step explanation:

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Step-by-step explanation:

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