SSC CGL 202061)If \(P={x^3+y^3\over (x-y)^2+3xy}\) , \(Q={(x+y)^2-3xy\over x^3-y^3}\) and \(R={(x+y)^2+(x-y)^2\over x^2-y^2}\), then what is the value of \((P\div Q)\times R\) ?
\(2(x^2+y^2)\)
\((P\div Q)\times R\) \(={x^3+y^3\over (x-y)^2+3xy}\div {(x+y)^2-3xy\over x^3-y^3}\times {(x+y)^2+(x-y)^2\over x^2-y^2}\)
\(={(x+y)(x^2+y^2-xy)\over x^2+y^2-2xy+3xy}\times {(x-y)(x^2+y^2+xy)\over x^2+y^2+2xy-3xy}\times {x^2+y^2+2xy+x^2+y^2-2xy\over (x+y)(x-y)}\)
= \(2(x^2+y^2)\)
SSC CHSL 202162)Simplify the following expression. (2x - 3y)3 - 18xy (2x - 3y)
8x3 - 72x2y + 108xy2 - 27y3
SSC CHSL 202163)If \(x^2- 6√3 x + 1 = 0\), then the value of \(\rm x^3 + \frac{1}{x^3}\) will be :
630√3
SSC CHSL 202164)If x4 + y4 + x2y2 = 117 and x2 + y2 - xy = 3(4 + √3), then the value of (x2 + y2) will be:
12
SSC CHSL 202165)If (a + b + c) = 0 and (abc) = 12, then what is the value of (a3 + b3 + c3)?
36
SSC CHSL 202166)If \(\rm x^4-\frac{1}{x^4} = 6887\), then the positive value of \(\rm x-\frac{1}{x} \) is:
9
SSC CHSL 202167)If x - y - z = 0, then the value of (x2 + y2 + z2) ÷ (y2 + xz) is:
2
SSC CHSL 202168)The value of \(\left(4\frac{3}{5}+7\frac{2}{5}\right) + \left(7\frac{1}{6}-2\frac{1}{3}\right)\) of is:
8
SSC CHSL 202169)If x2 - 3x + 1 = 0, then the value of \(\rm 2(x^8+\frac{1}{x^8}) - 5(x^2+\frac{1}{x^2})\) is:
4379
SSC CHSL 202170)If a + b + c = 5 and a3 + b3 + c3 - 3abc = 185, then the value of ab + bc + ac lies between:
-7 and -3