State whether the following quadratic equations have two distinct real roots. Justicy your answer: `(x-sqrt(2))^(2)-2(x+1)=0`

Explanation

Given equation is `(x-sqrt(2))^(2) -sqrt(2)(x+1)=0`
`implies x^(2)+(sqrt(2))^(2)-2xsqrt(2)-sqrt(2)x-sqrt(2)=0 [ :' (a-b)^(2)=a^(2)-2ab+b^(2)]`
`implies x^(2)+2-2sqrt(2)x-sqrt(2)x-sqrt(2)=0`
`implies x^(2)-3sqrt(2)x+(2-sqrt(2))=0`
on comparing with `ax^(2)+bx+c=0` we get
`a=1,b=3sqrt(2)` and `c=2-sqrt(2)`
`:.` Discriminant `D=b^(2)-4ac`
`=(-3sqrt(2))^(2)-4(1)(-sqrt(2))=9xx2-8+4sqrt(2)`
`=18-8+4sqrt(2)=10+4sqrt(2)gt0` i.e. `Dgt0`
Hene the equation `(x-sqrt(2))^(2)-sqrt(2)(x+1)=0` has two distinct real roots.