SSC CGL 201921)If \(x+y+z=2, \) \(xy+yz+zx=-11\) and \(xyz=-12\), then what is the value of \(\sqrt{x^3+y^3+z^3-2} \)?
6
SSC CGL 201922)If \(x^4-83x^2+1=0\), then a value of \((x^3-x^{-3})\) can be :
756
SSC CGL 201923)If \((5x+1)^3+\)\((x-3)^3+\)\(8(3x-4)^3=\)\(6(5x+1)(x-3)\)\((3x-4)\), then x is equal to :
\(5\over6\)
SSC CGL 201924)If \(8x^3-27y^3\)\(=(Ax+By)\)\((Cx^2-Dy^2\)\(+6xy)\), then \((A+B+C-D)\) is equal to :
12
SSC CGL 201925)If \(x={\sqrt5-\sqrt3\over\sqrt5+\sqrt3}\) and y is the reciprocal of x, then what is the value of \((x^3+y^3)\)?
488
\(x={\sqrt5-\sqrt3\over\sqrt5+\sqrt3}\); \(y={\sqrt5+\sqrt3\over\sqrt5-\sqrt3}\) Rationalize the equation we get
\(x = {4-\sqrt{15}}; y=4+\sqrt{15}\)
using identity \({a^3 + b^3} = ( a+ b )(a^2 +b^2 - ab)\)
\((x^3+y^3) = 488\)