2. Sample Papers
  3. SSC

SSC Sample Paper SSC CHSL (10+2) Sample Test Paper-2

  • question_answer
    If                                                                                    \[x+y+z=10\] ,                                                             \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=30\] , then find the value of                                                           \[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}+-3xyz\] .

    A)  50                               

    B)  -50  

    C)  40                   

    D)         -40

    Correct Answer: B

    Solution :

                                                                                         \[\because\]                                                     \[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz=(x+y+z)\]                                                         \[({{x}^{2}}+{{y}^{2}}+{{z}^{2}}-xy-yz-zx)\] -Formula We do not know the value of                                                                                     \[xy+yz+zx\] . First find it.                                                                                      \[\because\]                                               \[{{(x+y+z)}^{2}}={{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2\]                                                                                   \[(xy+yz+zx)-\] Formula                                                                     \[({{10}^{2}}=30+2(xy+yz+zx)\]                                                                                     \[\Rightarrow\]                                                                          \[2(xy+yz+zx)=100-30=70\]                                                                                      \[\therefore\]                                                                       \[xy+yz+zx=\frac{70}{2}=35\]                                                                                      \[\therefore\]                                                            \[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz\]                                                 \[=(x+y+z)({{x}^{2}}+{{y}^{2}}+{{z}^{2}}-xy-yz-zx)\]                                                                                    \[=10(30-35)\]                                                                                \[=10\times -5=-50\]


You need to login to perform this action.
You will be redirected in 3 sec spinner