Question

Please answer question in image.

Answer 1

Answer:

0

Step-by-step explanation:

 For convenience, let √x = a.

⇒ | a - 2 | + a( a - 4 ) + 2 = 0

⇒ | a - 2 | + a^2 - 4a + 2 = 0

     Now, two cases arise:

Case 1:

    ⇒ ( a - 2 ) + a^2 - 4a + 2 = 0

    ⇒ a - 2 + a^2 - 4a + 2 = 0

    ⇒ a^2 - 4a + a - 2 + 2 = 0

    ⇒ a^2 - 3a = 0

    ⇒ a( a - 3 ) = 0

    ⇒ a = 0 or  a = 3

This means, either √x = 0 or √x = 3. As given, x ≠ 0, therefore, √x = 3   ⇒ x = 9.

  Case 2:

    ⇒ - ( a - 2 ) + a^2 - 4a + 2 = 0

   ⇒ - a + 2 + a^2 - 4a + 2 = 0

   ⇒ a^2 - 4a - a + 2 + 2 = 0

   ⇒ a^2 - 4a - a + 4 = 0

   ⇒ a( a - 4 ) - ( a - 4 )  = 0

   ⇒ ( a - 4 )( a - 1 ) = 0

   ⇒ a = 4  or  a = 1

Thus, √x = 4  or  √x = 1  ⇒ x = 16  or x = 1.

But,

| √x - 2 | + √x( √x - 4 ) + 2 = 4 ≠ 0, for x = 16.

   Therefore, x = 1

Hence,

     Solutions for the given equation are 9 and 1.

Thus, k = 2    ⇒ k - 2 = 2 - 2 = 0   ⇒ k - 2 = 0

  Hence the required value of k - 2 is 0.

Answer 2

Answer:

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