Question

Answer this ...........
if x=1/√5-2 . find the value of x³-3x²-5x+3

Answer 1

Hey mate!

$x = \frac{1}{ \sqrt{5} - 2} \\ \\ x = \frac{1}{ \sqrt{5} - 2} \times \frac{ \sqrt{5} + 2}{ \sqrt{5} + 2} \\ \\ x = \frac{ \sqrt{5} + 2 }{5 - 4} = \sqrt{5} + 2$

x² = (√5 + 2)²

=> (√5)² + 2 × √5 × 2 + (2)²

=> 5 + 4√5 + 4

=> 9 + 4√5

Now,

x³ - 3x² - 5x + 3

=> (√5 + 2)(9 + 4√5) - 3(9+4√5) - 5(√5 + 2) +3

=> 9√5 + 20 + 18 + 8√5 - 27 - 12√5 - 5√5 - 10 + 3

$= > \cancel{17 \sqrt{5} } + 38 - \cancel{17 \sqrt{5} } - 34 \\ \\ = > 38 - 34 \\ \\ = > 4$

Therefore the answer is $\textbf{4.}$

Thanks for the question!

Answer 2

Heya!!

Thanks for asking the question.

Pls refer to the attachment for the solution.

Hope it helps you : ).