Question

If x = 7-4√3 then find value of x²+1/x²

Answer 1

Hope ! IT HELPS YOU

Answer 2

The value of x²+1/x² = 194

Given:

x = 7 - 4√3
To find:

The value of x²+1/x²

Solution:

Given  x = 7-4√3

⇒  $\frac{1}{x} = \frac{1}{7-4\sqrt{3} }$

To rationalize $\frac{1}{7-4\sqrt{3} }$ multiply and divide with (7+4√3)  

⇒ $\frac{1}{7-4\sqrt{3} }(\frac{7+4\sqrt{3} }{7+4\sqrt{3} } )$ = $\frac{7+4\sqrt{3} }{7^{2} - 16(3) }$ = $\frac{7+4\sqrt{3} }{49 - 48 }$ = $7+4\sqrt{3}$

⇒ 1/x = $7+4\sqrt{3}$  

Take (x+1/x)

⇒ (x+1/x)  = 7-4√3 + 7 + 4√3

⇒ (x+1/x) = 14

Do squaring on both side

⇒ (x+1/x)² = 14²  

⇒ x²+1/x² + 2(x)(1/x) = 196

⇒ x²+1/x² + 2 = 196

⇒ x²+1/x² = 196 - 2

⇒ x²+1/x² = 194

The value of x²+1/x² = 194

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