(x²+x)²-(x²+x)-2=o quadratic equation
solve it by reducing it to quadratic equation
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(x²+x)²-(x²+x)-2=o quadratic equation
solve it by reducing it to quadratic equation
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Step-by-step explanation:
Let (x² + x) be a.
So, the equation becomes,
a² - a - 2 = 0
a² - (2a - a) - 2 = 0
a² + a - 2a - 2 = 0
a(a + 1) - 2(a + 1) = 0
(a + 1) (a - 2) = 0
a + 1 = 0 or a - 2 = 0
a = -1 or a = 2
x² + x = -1 or x² + x = 2
x² + x + 1 = 0 or x² + x - 2 = 0
(here, find x using
quadratic formula)
x² + 2x - x - 2 = 0
x(x + 2) - 1(x + 2) = 0
(x - 1) (x + 2) = 0
x = 1, -2
Verified answer
Answer:
x = -2,1,[tex]\frac{-1 + i\sqrt{3} }{2}[/tex],[tex]\frac{-1 - i\sqrt{3} }{2}[/tex]
Step-by-step explanation:
(x²+x)²-(x²+x)-2= 0
let X = (x²+x)
Now the equation becomes,
X² - X - 2 = 0
=> X² - 2X + X - 2 = 0
=> X(X - 2) + X - 2 = 0
=> (X - 2)(X + 1) = 0
=> (X - 2) = 0 or (X +1)=0
=> x²+x-2 = 0 or x²+x+1 = 0
take x²+x-2 = 0,
=> x²+2x-x-2 = 0
=> x(x+2) - (x+2) = 0
=> (x+2)(x - 1) = 0
=> (x+2)= 0 or (x - 1) = 0
=> x= - 2 or x = 1
take x²+x+1 = 0
using formula,
x = [tex]\frac{-1 \pm \sqrt{1^2 - 4(1)(1)} }{2(1)}[/tex]
= [tex]\frac{-1 \pm \sqrt{1 - 4} }{2}[/tex]
= [tex]\frac{-1 \pm \sqrt{-3} }{2}[/tex]
= [tex]\frac{-1 \pm i\sqrt{3} }{2}[/tex]
= [tex]\frac{-1 + i\sqrt{3} }{2}[/tex] or [tex]\frac{-1 - i\sqrt{3} }{2}[/tex]
so, the solutions are, -2,1,[tex]\frac{-1 + i\sqrt{3} }{2}[/tex],[tex]\frac{-1 - i\sqrt{3} }{2}[/tex]