Question

If x=1/(2-V3) then find the
value of x2-4x+1 is equal to​

Answer 1

Answer:

The value of given polynomial is zero.

Step-by-step explanation:

$x=\frac{1}{2-\sqrt{3} } \\\\ rationalising \ factor= 2+\sqrt{3} \\\\ x =\frac{1}{2-\sqrt{3} } (\frac{2+\sqrt{3} }{2+\sqrt{3} } ) \\\\ x = \frac{2+\sqrt{3} }{2^{2} -(\sqrt{3}) ^{2} } \ [(a+b)(a-b) = a^{2} - b^{2} ]\\\\ x=\frac{2+\sqrt{3} }{4-3} = 2+\sqrt{3}$

given polynomial,

$x^{2} -4x+1 \\ => (2+\sqrt{3})^2 - 4(2+\sqrt{3} ) +1\\ => 2^{2} +\sqrt{3}^2 + 2(2)(\sqrt{3} ) -4(2+\sqrt{3})+1 \\ => 4+3+4\sqrt{3} -8-4\sqrt{3} +1\\=>7-8+1\\=>8-8\\=>0$