Question

If b = 3^1/3 +3, then b3 -9b2 + 27b is equal to​

Answer 1

Given: Value of b = 3^1/3 +3

To find: b^3 - 9b^2 + 27b is equal to​?

Solution:

• As we have given the value of b as 3^1/3 +3, so lets put it directly in the given equation, we get:

• b^3 -9b^2 + 27b = (3^1/3 +3)^3 - 9(3^1/3 +3)^2 + 27(3^1/3 +3)

• Now solving further we get:

        (3 + 27 + 9x3^2/3 + 27x3^1/3) - 9(3^2/3 + 9 + 6x3^1/3) + 27x3^1/3 + 81

Opening all the brackets, we get:

        30 + 9x3^2/3 + 27x3^1/3 - 9x3^2/3 - 81 - 54x3^1/3 + 27x3^1/3 + 81

After cancelling the terms, we get:

      = 30

Answer:

           So the value of b^3 - 9b^2 + 27b is equal to​ 30 if b =  3^1/3 +3.

Answer 2

Answer:

30

Step-by-step explanation:

$b = \sqrt[3]{3} + 3 \\ {b}^{3} - 9 {b}^{2} + 27b$

by putting the value we get :

${( \sqrt[3]{3} + 3) }^{3} - 9 {( \sqrt[3]{3} + 3) }^{2} + 27( \sqrt[3]{3} + 3) \\ = 3 + 27 + 9 \sqrt[3]{ {3}^{2} } + 27 \sqrt[3]{3} - 9\sqrt[3]{ {3}^{2} } - 81 - 54\sqrt[3]{3} + 27\sqrt[3]{3} + 81 \\ = 30 + 81 - 81- 54\sqrt[3]{3} + 27\sqrt[3]{3}+ 27\sqrt[3]{3}- 9\sqrt[3]{ {3}^{2} } + 9\sqrt[3]{ {3}^{2} } \\ \\ = 30$