Question

solve to find x :- x⁴-7x²-144=0

Answer 1

Let y = x².

Then the equation is y² - 7y - 144 = 0  

Use the quadratic formula to factor  

  ay²+by+c=0  

where  a=1  ,b=-7  ,c=-144  

y = [-b ± √(b²-4ac)] / (2a)  

  = [-(-7) ± √((-7)² - 4(1)(-144))] / 2(1)  

  = [7 ± √(625)] / 2  

  = [7 ± 25] / 2  

  = 3.5 ± 12.5  

So now

y₁ = 3.5 - 12.5 = -9  

y₂ = 3.5 + 12.5 = 16  

y² - 7y - 144 = (y-16)(y+9)  

And that

x⁴ - 7x² - 144 = (x²-16)(x²+9)  

= (x+4)(x-4)(x+3i)(x-3i)  

x = 4, -4, 3i, -3i