The operation *is defined by x*y=2x-y, where x and y are real numbers. Find the value of (i) y, if y *(3*y)=6

The value of y = 4

Step-by-step explanation:

Explanation:-

Given the operation *is defined by

         x*y=2 x-y,where x and y are real numbers

Given  y * ( 3 * y ) = 6

     ⇒    y * ( 2 (3) -y) = 6    (∵    x*y=2 x-y)

     ⇒     y * ( 6 - y) = 6

    ⇒     2 (y) - (6 - y ) = 6

    ⇒       2 y - 6 + y = 6

   ⇒         3 y = 6 + 6

  ⇒             3 y = 12

  ⇒               y = 4

Verification:-

Put y =4 in given operation

 L.H.S    

 y * ( 3 * y ) =  4 * ( 3 * 4)

                  = 4 * (2(3)-4)      (∵ x*y=2 x-y )

                 = 4 * ( 6-4)

                = 4 * 2            

               = 2(4) -2      (∵ x*y=2 x-y )

               = 6

              =R.H.S

  y *(3*y) = 6

          ∴ y = 4 is satisfied  

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step-by-step explanati∵∵∴∴on:

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1