Question

if x = if x=1/√5-2 then find x³-3²-5x+3 ​

Answer 1

Step-by-step explanation:

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

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

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

${x}^{2} = {( \sqrt{5} + 2) }^{2}$

$= > \: { \sqrt{5} }^{2} + 2 \times \sqrt{5} + (2) ^{2}$

$5 + 4 \sqrt{5} + 4$

$9 + 4 \sqrt{5}$

Now,

$x ^{3} - 3 {x}^{2} - 5x + 3$

$= ( \sqrt{5} + 2)(9 + 4 \sqrt{5} ) - 3(9 + 4 \sqrt{5} ) - 5( \sqrt{5} + 2) + 3$

$= 9 \sqrt{5} + 20 + 18 + 8 \sqrt{5} - 27 - 12 \sqrt{5} - 5 \sqrt{5} - 10 + 3$

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

$= 38 - 34$

$= 4$

The answer is 4.

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