Show that if the axes be turned through `7(1^(@))/(2)`, the equation `sqrt(3)x^(2)+(sqrt(3)-1)xy-y^(2)=0` become free of xy in its new form.

For the equation 2x^(2)-6sqrt(2)x-1=0

Solve the equation 3sqrt((x+3))-sqrt((x-2))=7

Prove that if the axes be turned through (pi)/(4) the equation x^(2)-y^(2)=a^(2) is transformed to the form xy = lambda . Find the value of lambda .

Solve the equation sqrt((6-x))(3^(x^(2)-7.2x+3.9)-9sqrt(3))=0

The roots of the equation x^(2)-2sqrt(3)x+3=0 are

Though what angle should the axes be rotated so that the equation 9x^2 -2sqrt3xy+7y^2=10 may be changed to 3x^2 +5y^2=5 ?

The number of solutions of the equation sqrt(x^(2))-sqrt((x-1)^(2))+sqrt((x-2)^(2))=sqrt(5) is

The equation 3ax^2+9xy+(a^2-2)y^2=0 represents two perpendicular straight lines for

Solve the equation (2+sqrt(3))^(x^(2)-2x+1)+(2-sqrt(3))^(x^(2)-2x-1)=101/(10(2-sqrt(3))

The equation x+2y=3,y-2x=1 and 7x-6y+a=0 are consistent for