Question

If x=7+4 root 3, find the value of x square +1/x square

Answer 1

Given=7+4√3

x²=(7+4√3)²= 7²+4√3²+2×4√3×7
=49+16×3+14×4√3
=97+56√3
rationalize
1/x²=97-(56√3)/97²-56√3²
=97-(56√3)/1
=97-56√3

x²+1/x²= 97+56√3+(97-56√3)
= 97+97
=194
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Answer 2

Answer:

The value is $14$.

Step-by-step explanation:

It is given that $x=7+4\sqrt{3}$.

We need to determine $x+\frac{1}{x}$

If $x=7+4\sqrt{3}$

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

Rationalizing

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

$=7-4\sqrt{3}$

Adding both equations, we get

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

$=14$

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