Question

(x²+x)²-(x²+x)-2=0 ans :- 1,-2​

Answer 1

꧁༺Question༻꧂

Solve:(x²+x)²-(x²+x)-2=0

꧁༺Answer༻꧂

(x²+x)²-(x²+x)-2=0

Let's x²+x=A, then put the value

➟A²-A-2=0

➟A²-(2-1)A-2=0

➟A²-2A+A-2=0

➟A(A-2)+1(A-2)=0

➟(A-2)(A+1)=0

from A=2 or,x²+x=2 (i)

from equation (i)

➟x(x+1)=2 {x+1=2⇒x=1}

➟ x=2 and 1

fromA=-1 or x²+x=-1 (ii)

from equation (ii),

x(x+1)=-1 {x+1=-1⇒x=-1}

x=-1 and -2

So,x=±1 and ±2

Answer 2

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(x²+x)²-(x²+x)-2=0

Let's x²+x=A, then put the value

A²-A-2=0

A²-(2-1)A-2-0

A²-2A+A-2=0

A(A-2)+1(A-2)=0

(A-2)(A+1)=0

from A=2 or, x²+x=2 (i)

from equation ____(i)

x(x+1) = 2

X = 2 and 1

from A = -1 or x²+x=-1 (ii)

from equation (ii),

x(x+1) = - 1

x=-1 and -2

So,x=+1 and ±2

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