Question

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Answer 1

Explanation:

Let p(x) = 3x² - 2x - 3=0

On comparing the given equation with quadratic equation ax² + bx + c = 0,

we have a = 3, b = -2 and c = -3.

By using quadratic formula,

x = - b ± √b² - 4ac / 2a

=-(-2) ± √(-2)²-4 (3) (3)/2 (3)

= 2 ± √4-36/6 (*-*-=+)

= 2 ± √-32/6 is the answer.a = √3+1

.. a4 +16/ a^, we can write as

= ( a² + 4/a²)² - 2 (a²) (4/a²)

= ( a² + 4/a²) - 8

a² = ( √3+ 1)² = ( √3 )² + 1² + 2 (√3 ) ( 1 ) = 3+1+ 2√3=4+2√3.

4/a²=4/(4+2√3)

= [4 / (4+2√3)] ×[(4-2√3)/(4-2√3)] (*. Rationalise the denominator)

= [4 (4-2√3)] / [( 4+2√3)( 4-2√3)] = [4 (4-2√3)] / [(4)²-(2√3)²] [*•* a² -

b² = (a - b)(a + b)]

= [4 (4-2√3)]/(16 - 12)

= [4 (4-2√3)]/(4)

=4-2√3

(a²-4/a²)² - 8

= [4+2√3-(4-2-√3) 1² - 8

= [4+2√3-4+2√3]²-8__(¨¨*-* + :

+)

= [2√3+2√31²-8

= [4√3 ]² - 8

= 48 - 8

= 40 is the answer.

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