Question

If (x+2) = (x2-1) x, then find the nature of the equation.​

Answer 1

Answer:

Given equation is (x

2

+1)

2

−x

2

=0

⇒(x

2

)

2

+(1)

2

+2(x)

2

(1)−x

2

=0

⇒(x

2

)

2

+x

2

+1=0

Let x

2

=y

⇒y

2

+1y+1=0

Now, D=b

2

−4ac

⇒D=(1)

2

−4(1)(1)=1−4

⇒D=−3

⇒D<0

So, the given equation y

2

+y+1=0 has no real roots.

∴ the equation $$\left ( x^{2} + 1 \right )^{2} - x^{2} =0$ has no real roots.

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