1Plzzzz someone solve the second one
just give me the hint.
1) Show that the soln set of eqns
(x+1) 2 + [x-1] 2 = (x-1)2 + [x+1] 2 , where [x] and (x) are the gratest integer and nearest integer to x
, is x belonging to I.
2) If P(x) = ax 2+bx+c and Q(x) = -ax 2+dx+c, where ac≠0, then show that P(x)Q(x) = 0 has at leat two real roots.
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4 Answers
1ans 1)
as we know that [x-1]=[x]-1
and [x+1]=[x]+1
therefore now expanding on both sides
(x^2)+1+2x +([x]^2) +1-2[x]=(x^2)+1-2x + ([x]^2) +1-2[x]
which gives
4x=4[x]
which is only possible for integral values of x
