IIT JEE , AIEEE Forum - Mathematics , Algebra

DON007

²hey .............look...............

using above equation we get...........

+

= -2a........(1)

=b.....(2)

now we have to quad. equation with rational coefficient and one of whose roots is

+

²+,given that

² +

² is not a perfect square.

so..........we have studied if one root is a+sqrtb

then other root is a-sqrtb

so other root of this equation is.............

+

-

²+².

so forming the equation ........

x² - (sum of roots)x + product of roots=0

x²- [(

+

²+² ) + (

+

-

²+²)]x + [ (+

+

²+ ² ) (

+

²+2 ) ]=0

_{x²- 2 (+)x +( +)}2 _{- (}2₊2₎₌₀

_x2 _{- 2(-2a)x + 2}₌₀

_x2_{+4ax + 2b=0 ............ans}

_thanks