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Alenkinab [10]
3 years ago
15

How do you do x ^4-4? What is the x values?

Mathematics
1 answer:
VladimirAG [237]3 years ago
3 0
We know that
A difference of two perfect squares (A² - B²)  <span>can be factored into </span><span> (A+B) • (A-B)
</span> then
x ^4-4--------> (x²-2)*(x²+2)
(x²-2)--------> (x-√2)*(x+√2)
x1=+√2
x2=-√2

the other term
(x²+2)=0-> x²=-2-------------- x=(+-)√-2

i <span> is called the </span><span>imaginary unit. </span><span>It satisfies </span><span>  i</span>²<span>  =-1
</span><span>Both </span><span>  i </span><span>  and </span><span>  -i </span><span>  are the square roots of </span><span>  -1 
</span><span>√<span> -2 </span></span> =√<span> -1• 2  </span><span> = </span>√ -1 •√<span>  2  </span> =i • <span> √<span> 2 </span></span>
The equation has no real solutions. It has 2 imaginary, or complex solutions.
x3=  0 + √2<span> <span>i  
</span></span>x4=  0  - √2<span> i </span>

the answer is 

the values of x are
x1=+√2
x2=-√2
x3=  0 + √2 i  
x4=  0  - √2 i

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