Question

x
$x = 9 - 4 \sqrt{5 \: } find \: {x }^{2} + \frac{1}{x {}^{2} }$
​

Answer 1

Answer:

Hope you liked my answer plz mark my answer brainliest ✌

Answer 2

Question :--- if x = 9 - 4√5 , find (x² + 1/x²) = ?

Solution :---

→ x = (9-4√5)

→ 1/x = 1/(9-4√5)

Rationalizing the RHS part now ,

→ 1/x = 1/(9 - 4√5) * (9+4√5)/(9+4√5)

using (a+b)(a-b) = a² - b² in Denominator now,

→ 1/x = (9 + 4√5) / (9² - (4√5)²)

→ 1/x = (9+4√5) / (81-80)

→ 1/x = (9+4√5)

So ,

→ x + 1/x = (9-4√5) + (9-4√5)

→ x + 1/x = 18

Squaring both sides now we get,

→ (x+1/x) ² = (18)²

using (a+b)² = a² + b² +2ab in LHS,

→ x² + 1/x² + 2 * x * 1/x = 324

→ x² + 1/x² + 2 = 324

→ x² + 1/x² = 324 - 2

→ x² + 1/x² = 322 (Ans) .