Question

if x 9+4√5, find the value of x square +1/x square​

Answer 1

ANSWER:

• Value of x² +1/x² is 322.

GIVEN:

• x = 9+4√5

TO FIND :

• Value of x²+ 1/x²

SOLUTION:

=> x = 9+4√5

Finding 1/x:

$\implies \: \dfrac{1}{x} = \dfrac{1}{9 + 4 \sqrt{5} } \\ \\ \implies \: \dfrac{1}{x} = \dfrac{1}{9 + 4 \sqrt{5} } \times \dfrac{9 - 4 \sqrt{5} }{9 - 4 \sqrt{5} } \\ \\ \implies \: \dfrac{1}{x} = \dfrac{9 - 4 \sqrt{5} }{81 - 80} \\ \\ \implies \: \dfrac{1}{x} = 9 - 4 \sqrt{5}$

Value of 1/x = 9-4√5

=> x²+ 1/x² = (9+4√5)²+(9-4√5)²

=> x² +1/x² = 81+80+72√5+81+80-72√5

=> x²+ 1/x² = 322.

NOTE:

Some important formulas:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

(a+b)(a-b) = a²-b²

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

a³+b³ = (a+b)(a²+b²-ab)

a³-b³ = (a-b)(a²+b²+ab)

(a+b)² = (a-b)²+4ab

(a-b)² = (a+b)²-4ab