Question

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Answer 1

If a=3+√7/2, find the value of a²+1/2

a = (3 + √7)/2

1/a = 2/( 3 + √7)

=2(3 - √7)/( 3 + √7)(3 -√7)

=2(3 - √7)/(3² -√7²)

=2(3 -√7)/2

=(3 - √7)

now,

a² + 1/a² = (a + 1/a)² -2a.1/a

=(a +1/a)² -2

={ (3 + √7)/2 + (3 - √7)}² -2

={ (3 +√7 +6 -2√7)/4 - 2

={( 9 -√7)² - 8}/4

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