Question

If x=-5+2√-4,find the value of x⁴+9x³35x²-x+4

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

x = 5 + 2√-4

★We may also write it as :-

x - 5 = 2√-4

★Here

★When we try to solve it then it is necessary to squarring both sides :-

So,

(x + 5)² = (2√-4)²

★Notation :-

★We know that

i² = -1

★We may write it as :-

x² + 25 + 10x = (2 × 2i)²

x² + 25 + 10x = 16i²

x² + 25 + 10x = -16

x² + 10x + 41 = 0

★Hence,

Equation :- x⁴ + 9x³ + 35x² - x + 4.

= x⁴ + 10x³ - x³ + 41x² - 10x² + 4x² - 41x + 40x + 164 - 160

= x⁴ + 10x³ + 41x² - x³ - 10x² - 41x + 4x² + 40x + 164 - 160

= x²(x² + 10x + 41) - x(x² + 10x + 41) + 4(x² + 10x + 41) - 160

= x²(0) - x(0) + 4(0) - 160

= -160

$\Large{\fbox{Hence\;we\;get\;=\;-160}}$