What is (-1/2+(sqrt(3))/2)^2 ?

The solution to (-1/2+(sqrt(3))/2)^2 is (2-sqrt(3))/2

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simplify (-1/2+(sqrt(3))/2)^2

simplify

(- \frac{1}{2} + \frac{3}{2})^{2}

\frac{2 - 3}{2}

Solution steps

(- \frac{1}{2} + \frac{3}{2})^{2}

- \frac{1}{2} + \frac{3}{2} = \frac{- 1 + 3}{2}

= (\frac{- 1 + 3}{2})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( - 1 + 3 ) ^{2}}{2 ^{2}}

2^{2} = 4

= \frac{( - 1 + 3 ) ^{2}}{4}

(- 1 + 3)^{2} = 4 - 23

= \frac{4 - 2 3}{4}

Factor

4 - 23 : 2 (2 - 3)

= \frac{2 ( 2 - 3 )}{4}

Cancel the common factor:

2

= \frac{2 - 3}{2}

(3 x + 1) (3 x + 1)

4 + \frac{9}{4}

5 + \frac{1}{5} - \frac{1}{15} - [1 - (\frac{4}{90} - 0.7 + 1.71)]

\frac{1}{5 + 3}

(2 x^{2} - 3 x) (3 x^{2} + 2 x - 1)

What is (-1/2+(sqrt(3))/2)^2 ?
The solution to (-1/2+(sqrt(3))/2)^2 is (2-sqrt(3))/2