1.

`(x^(2)+1)^(2)-x^(2)=0` has (i) four real roots (ii) two real roots (iii) no real roots (iv) one real root

Answer» Given equation is `(x^(2)+1)^(2)-x^(2)=0`
`implies(x^(2)+1-x)(x^(2)+1+x)=0`
`impliesx^(2)+1-x=0orx^(2)+1+x=0`
For first equation `x^(2)+1-x=0`
i.e., `x^(2)+1+x=0`
`D=(-1)^(2)-4(1)(1)=1-4=-3lt0`
`implies` Equation has no real root.
For second equation `x^(2)+1+x=0`
i.e., `x^(2)+x+1=0`
`D=(1)^(2)-4(1)(1)=1-4=-3lt0`
`implies` Equation has no real root.
Hence, given equation has no real root.


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