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
