Question

x²+1/x²-2-3x+3/x
Factorise it
And do in the copy
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Answer 1

Answer:

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Answer 2

Answer:

x= 1 , -1 , 3+√13 /2 , 3-√13 /2

Step-by-step explanation:

Let, p(x) =0

x²+(1/x²) -2-3x+(3/x) =0

x²-3x-2+1/x²+3/x =0

x²-3x-2+1/x²(1+3x) =0

1/x² (x⁴-3x³-2x²+3x+1 ) =0

1/x² [x⁴-3x³-x²-x²+3x+1] =0

1/x² [x²(x²-3x-1) -1(x²-3x-1)] =0

1/x² [(x²-3x-1)(x²-1)] =0

(x²-3x-1)[ 1/x²(x²-1)] =0

(x²-3x-1) (1-1/x²) =0

x²-3x-1=0 Or 1-1/x²=0 => 1/x²=1 => x²=1 => x=±1

=>We know that,

∆=b²-4ac =(-3)²-4(1)(-1) =9+4= 13 >0

=>(alpha,beta) = -b±√∆ /2a = -(-3)±√13 /2(1) = 3±√13 /2

=>we get,

alpha = 3+√13 /2 ; beta = 3-√13 /2

=>Now,

alpha×beta = c/a = -1/1 = -1

alpha+beta = -b/a = -(-3)/1 = 3

=>We get,

x= 1 , -1

x= 3+√13 /2 , 3-√13 /2