Question

Simplify(1-√3)(1/3+√3) leaving your answer in the form p +q √3
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Answer 1

-8/3 + 2/3 (√3)

Where, p = -8/3

q = 2/3

Explanation:

Simplify(1-√3)(1/3+√3)

= (1-√3)(1/3+√3)

Expand the bracket

= 1(1/3+√3) -√3(1/3+√3)

= 1/3 + √3 - √3/3 - 3

Collect like terms

= 1/3 - 3 + √3 - √3/3

= (1/3 - 3) + (√3 - √3/3)

= -8/3 + [(3√3 - √3)/3]

= -8/3 + 2√3/3

= -8/3 + 1/3( 2√3)

= -8/3 + 2/3 (√3)

Where, p = -8/3

q = 2/3