Question

If × = 5 - root 24 then find × cube minus 1 by x cube

Answer 1

Answer:

Given:

• x = 5 - √24

To find:

• the value of $x^3-1$

Solving Question:

 identity = $x^3-y^3= (x-y)(x^2+xy+y^2)$

Let's simplify question;

⇒ x = 5 - √24

⇒ x = 5 - √6*4

⇒ x = 5 - 2√6

Solution:

substitute it in the question ;

⇒  $x^3-y^3= (x-y)(x^2+xy+y^2)$

here, x = 5 - 2√6 ; y = 1

⇒ ( 5 - 2√6 - 1) ( (5-2√6)² + (5-2√6)(1) + 1² )

⇒ ( 4 - 2√6)((25 - 20√6 + 24 + 5 -2√6 +1) [ ∵ (a-b)² = a²-2ab +b² ]

⇒ (4-2√6)(25+24+5+1-20√6-2√6)

⇒ (4-2√6)( 55 -22√6 )

⇒ 4 - 88√6 -110√6 +264

⇒ 484 - 198√6

Thus,  answer is 484 - 198√6.