ques 74

Dear Student,

Please find below the solution to the asked query:

Given :  If ( x + y )³  - ( x - y )³  - 6 y ( x²  - y²) = k y² 

We know : ( a + b )³ = a³ + b³ + 3 a² b + 3 ab²  and ( a - b )³ = a³ - b³ - 3 a² b + 3 ab²  ,

Now we take L.H.S and use above identities and get :

( x + y )³  - ( x - y )³  - 6 y ( x²  - y²)

$\Rightarrow$( x³ + y³ + 3x² y + 3 x y²) - ( x³ - y³ - 3x² y + 3 x y²) - 6 y ( x²  - y²)

$\Rightarrow$x³ + y³ + 3x² y + 3 x y²-  x³ + y³ + 3x² y - 3 x y² - 6 x²  y  + 6 y³  

$\Rightarrow$  8 y³  , Now we compare that with R.H.S. and get

k = 8

Theerfore,

Option ( d )                                                                         ( Ans )

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