Subham Chakravarti

Hello Abhishree,

Being an Engineering student currently in my final year and also a part-time Mathematics tutor, I think that I can answer this question.

During the prevailing conditions outside, you, being a student, should be having mixed feelings staying indoors. The only reference to your studies are books, the Internet - Google, Youtube, etc. But some subjects need better understanding which goes much beyond mere videos and books, for example, Mathematics, which involves doubt clearing and concept boosting thus making the layers of your foundation stronger.

With the technology being so advanced nowadays and video calling applications like Zoom, Cisco Webex, Skype, Google Meet, etc. and the options of sharing the screen, I think that it is innovative and advisable for the online  tuitions . It is no different from offline teachings. The only difference being you are seeing your mentor virtually. This method of flowing of knowledge and education makes studying more enjoyable.

Good luck and happy learning.

All the Best! 

5(x² + y² + z²) = 4(xy + yz + zx)

or, 5x² + 5y² + 5z² = 4xy + 4yz + 4zx

or, 4x² + 4y² + 4z² + x² + y² + z² = 4xy + 4yz + 4zx

or, (4x² – 4xy + y²) + (4y² – 4yz + z²) + (4z² – 4zx + x²) = 0

or, (2x - y)² + (2y - z)² + (2z - x)² = 0

We know that, since sum of squares is 0, each square must be equal to 0.

Therefore,
                   (2x - y)² = (2y - z)² = (2z - x)² = 0

             or, (2x - y) = (2y - z) = (2z - x) = 0

Therefore,

                       2x = y, 2y = z, 2z = x.

Thus converting all terms in respect to ‘x’ we get,
                                           y = 2x
                                           z = x/2
Therefore,
                   x : y : z = x : 2x : x/2
                                = 1 : 2 : ½
                                = 2 : 4 : 1

Answer:      x : y : z = 2 : 4 : 1

5(x² + y² + z²) = 4(xy + yz + zx)

or, 5x² + 5y² + 5z² = 4xy + 4yz + 4zx

or, 4x² + 4y² + 4z² + x² + y² + z² = 4xy + 4yz + 4zx

or, (4x² – 4xy + y²) + (4y² – 4yz + z²) + (4z² – 4zx + x²) = 0

or, (2x - y)² + (2y - z)² + (2z - x)² = 0

We know that, since sum of squares is 0, each square must be equal to 0.

Therefore,
                   (2x - y)² = (2y - z)² = (2z - x)² = 0

             or, (2x - y) = (2y - z) = (2z - x) = 0

Therefore,

                       2x = y, 2y = z, 2z = x.

Thus converting all terms in respect to ‘x’ we get,
                                           y = 2x
                                           z = x/2
Therefore,
                   x : y : z = x : 2x : x/2
                                = 1 : 2 : ½
                                = 2 : 4 : 1

Answer:      x : y : z = 2 : 4 : 1