Algebra> In the listed image can you tell me how b...

In the listed image can you tell me how beta*gamma = 2 ….. . . .. ??

Anshuman Mohanty , 8 Years ago

Grade 12th pass

5 Answers

Ajay

Last Activity: 8 Years ago

The value of gamma is not clear in image, could you mention what gamma us equal to...................

Anshuman Mohanty

Last Activity: 8 Years ago

Yes sorry..... . . . .it is not so clear.. ok the values are beta = α + α^2 + α^4 and gamma = α^3 + α^5 + α^7

Anshuman Mohanty

Last Activity: 8 Years ago

PLease answer. . . .. ….................................................................................

Ajay

Last Activity: 8 Years ago

The value of gamma is still not correct, either printing mistake or you gave me wrong value.

The correct value of gamma is below

$\beta =\alpha +{ \alpha }^{ 2 }+{ \alpha }^{ 4 }\quad and\quad \gamma \quad =\quad { \alpha }^{ 3 }+{ \alpha }^{ 5 }+{ \alpha }^{ 6 }\\ now\quad 1,\quad \alpha ,\quad { \alpha }^{ 2 },{ \alpha }^{ 4 },\quad { \alpha }^{ 3 },{ \alpha }^{ 5 },{ \alpha }^{ 6 }\quad are\quad 7th\quad roots\quad of\quad unity\\ we\quad have\quad 1+\alpha +{ \alpha }^{ 2 }+{ \alpha }^{ 3 }+{ \alpha }^{ 4 }+{ \alpha }^{ 5 }+{ \alpha }^{ 6 }\quad =\quad 0\quad -------------(1)\\ and\quad { \alpha }^{ 7 }\quad =\quad 1,\quad { \alpha }^{ 8 }\quad =\quad { \alpha },\quad { \alpha }^{ 9 }\quad =\quad { \alpha }^{ 2 }\quad etc----------(2)\\ \beta \gamma \quad =\quad { \alpha }^{ 4 }+{ \alpha }^{ 6 }+{ \alpha }^{ 7 }+{ \alpha }^{ 5 }+{ \alpha }^{ 7 }+{ \alpha }^{ 8 }+{ \alpha }^{ 7 }+{ \alpha }^{ 9 }+{ \alpha }^{ 10 }$

$from\quad (2)\\ \quad \quad \quad =\quad { \alpha }^{ 4 }+{ \alpha }^{ 6 }+1+{ \alpha }^{ 5 }+1+{ \alpha }+1+{ \alpha }^{ 2 }+{ \alpha }^{ 3 }\\ \quad \quad \quad =\quad 1+\alpha +{ \alpha }^{ 2 }+{ \alpha }^{ 3 }+{ \alpha }^{ 4 }+{ \alpha }^{ 5 }+{ \alpha }^{ 6 }+2\\ \quad \quad \quad \quad \quad use\quad value\quad from\quad eq\quad (1)\\ \quad \quad =\quad 2$