If x=√((3+√(5))/(3-√(5))) , then determine the value of x² - x - 8?

If x=√((3+√(5))/(3-√(5))) , then determine the value of x²…

If $x=\sqrt{\frac{3+\sqrt{5}}{3-\sqrt{5}}}$ , then determine the value of x² - x - 8?

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Correct answer: B

Explanation

The correct answer is option 2 i.e. √5 - 6.

$x=\sqrt{\frac{3+\sqrt{5}}{3-\sqrt{5}}}=\sqrt{\frac{(3+\sqrt5)^2}{4}}$

⇒ $x^2=\frac{(3+\sqrt5)^2}{4}=\frac{7+3\sqrt5}{2}$

Now, x² - x - 8

$=\frac{7+3\sqrt5}{2}-\frac{3+\sqrt5}{2}-8$

$=\frac{7+3\sqrt5-3-\sqrt{5}-16}{2}$

= (2√5 - 12)/2

= √5 - 6