Question

if x=7+4√3, find the value of x²+1/x²​

Answer 1

Answer:194

Step-by-step explanation:

x=7+4√3

1/X= 1/(7-4√3), on rationalization

1/X= 1/(7+4√3) × (7-4√3)/7-4√3)

= (7-4√3) /[7^2-(4√3)^2]

= 7-4√3/(49-48) = 7-4√3

X+1/X= 7+4√3 +7-4√3= 14

Using, a^2+b^2= (a+b)^2-2ab

So, x²+1/x²= (x+1/x)^2-2=

x²+1/x² = (14)^2 -2= 196-2= 194

Answer 2

                $x=7+4\sqrt{3} \\\\\frac{1}{x}=\frac{1}{7+4\sqrt{3}} \\\\Now*rationalize*the*denominator\\\\\frac{1}{x} =\frac{1}{7+4\sqrt{3}} *\frac{7-4\sqrt{3}}{74\sqrt{3}} \\\\\frac{1}{x}=\frac{7-4\sqrt{3}}{49-48} \\\\\frac{1}{x} = \frac{7-4\sqrt{3}}{1}\\\\ \frac{1}{x}=7-4\sqrt{3}$

               $x^{2} +(\frac{1}{x} )^{2}\\\\=(x+\frac{1}{x} )^{2}-2\\\\=(7+4\sqrt{3}+7-4\sqrt{3} )^{2}-2\\\\=(14)^{2}-2\\\\=196-2\\\\=194$

----- $\mathbf{From*Tharun *Kumar*Yadav}$  Hope helps you ----