If x=3+313+323, then x3−9×2+18x−12=

If $x = 3 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}}$ , then $x^{3} - 9 x^{2} + 18 x - 12 =$

A
1
B
2
C
3
D
0

Solution:

$x = 3 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}}$

$x - 3 = 3^{\frac{1}{3}} + 3^{\frac{2}{3}} [∵ {(a + b)}^{3} = a^{3} + b^{3} + 3 a b (a + b)]$

Cubing on both sides

${(x - 3)}^{3} = {(3^{\frac{1}{3}} + 3^{\frac{2}{3}})}^{3}$

$\Rightarrow x^{3} - 27 - 9 x^{2} + 27 x = 3 + 3^{2} + 9 (x - 3)$ $(∵ x - 3 = 3^{\frac{1}{3}} + 3^{\frac{2}{3}})$

$x^{3} - 9 x^{2} + 18 x - 12 = 0$

Related content

Types of Computers – Uses & Functions | Questions of Different Types of Computers

Important Questions for Class 12 Computer Science (C++) – Communication Technologies

KPSC Full Form – Kerala Public Service Commission

Holi Essay in Hindi: होली पर आकर्षक निबंध

BBL Full Form in Cricket – Big Bash League

How Sri Chaitanya is Guiding Students Towards Crack JEE 2024 in First Attempt?

Lachit Borphukan Essay in English

Leave Application for Teacher to Principal for Urgent Work, Out of Station, Sick Leave

How to Join The Indian Navy? Overview, Branches, Eligibility, Selection Procedures, Training, Career

History of Computers: Operating Systems, Parts, Networking