Question

If x = (2+√3), find the value of (x^2+1/x^2)

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Answer 1

Answer:

x = (2+√3)

We need to find x²+1/x²

Substitute the values.

$\to (2+\sqrt{3} )^{2}+\frac{1}{(2+\sqrt{3} )^{2}}$

If you solve (2+√3)² with concentration, you will get 7+4√3. We can rewrite the above equation as:

$\to 7+4\sqrt{3} +\frac{1}{7+4\sqrt{3} }$ -----(1)

Rationalise $\frac{1}{7+4\sqrt{3} }$. You will get:

$\frac{1}{7+4\sqrt{3} }=7-4\sqrt{3}$.

Thus, we can rewrite equation (1) as:

$\to 7+4\sqrt{3} +7-4\sqrt{3}$   [4√3-4√3=0]

$\to 14$

HOPE THIS HELPS :D