Question

X^2+xy-21=0 and xy-2y^2+20 =0 we get root are
(a) +1,+ 2 and -1,-2
(b) +2, +3 and -2,-3
(c) +3, +4 and -3,-4
(d) None
solve it by any simple method.​

Answer 1

Step-by-step explanation:

x^2 + xy -21 =0

- 2y^2 + xy +20 =0

or x^2+ 2y^2 = 41 or x^2 = 41- 2y^2

x= { 41 - 2y^2}^1/2

so 41- 2y^2 + { 41-2y^2}^1/2 y -21 =0

so ( 20 - 2y^2)^2 = y^2 { 41-2y^2}

400- 80 y^2 + 4y^4 = 41 y^2 - 2y^4

or 6 y^4 - 121y^2 + 400 =0

or y^2 = [ 121 +_ sqrt{ 121^2 - 4*6*400}]/12

=[ 121 +_ 71]/12

or y^2 =[ 121+ 71]/12= 192/12 & Y^2 =[21-71]/12 = 50/12

or y^2= 16 & y^2 = 25/6 or y= 5/sqrt6

or y = +_ 4 & x^2 = 41- 100/12

so x^2 = 41 - 32= 9 & x^2= 392/12=98/3

x= +-3 & x= sqrt (98/3)

so x = +_ 3 & sqrt(98/3)& y = +_ 4 & 5/sqrt6

DEADSOUL