Question

if x=1/√5-2 then find x³-3²-5x+3 ​

Answer 1

Step-by-step explanation:

Hey mate!

\begin{gathered}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\end{gathered}

x=

5

−2

1

x=

5

−2

1

×

5

+2

5

+2

x=

5−4

5

+2

=

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

\begin{gathered}= > \cancel{17 \sqrt{5} } + 38 - \cancel{17 \sqrt{5} } - 34 \\ \\ = > 38 - 34 \\ \\ = > 4\end{gathered}

=>

17

5

+38−

17

5

−34

=>38−34

=>4

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