Question

if a= 1/2-under root 3 find the value of a square - 4a+1​

Answer 1

$a = \frac{1}{2 - \sqrt{3} }$

$= \frac{2 + \sqrt{3} }{4 - 3} = \frac{2 + \sqrt{3} }{1}$

${a}^{2} = 4 + 3 + 4 \sqrt{3} = 7 + 4 \sqrt{3}$

${a}^{2} - 4a + 1 =$

$7 + 4 \sqrt{3} - 8 - 4 \sqrt{3} + 1$

=0

Answer 2

Given a = 2 + √3 ⇒ (1/a) = 1 / (2 + √3) Multiply and divide by (2 − √3) ⇒ (1/a) = (2 − √3) / [(2 + √3)(2 − √3)] ⇒ (1/a) = (2 − √3) / [4 − 3] ⇒ (1/a) = (2 − √3) ∴ a + (1/a) = (2 + √3) + (2 − √3) = 4

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