Question

If alpha and beta are tye roots of the equation x²-6x+4=0, find the value of (Alpha /beta +beta alpha) +2 (1/alpha +1/beta) + 3alphabeta​

Answer 1

EXPLANATION.

→ Let a and b are the roots of the equation

x² - 6x + 4 = 0.

→ (a/b + b/a) + 2 ( 1/a + 1/b) + 3ab.

→ sum of zeroes of a quadratic equation.

a + b = -b/a

a + b = 6 ......(1)

→ products of zeroes of a quadratic equation.

ab = c/a

ab = 4 ...... (2)

→ ( a/b + b/a) + 2(1/a + 1/b ) + 3ab.

→ Factories the equation. we get,

→ [ a² + b² / ab ] + 2 [ b + a / ab ] + 3ab.

→ [ ( a + b)² - 2ab / ab ] + 2 [ b + a / ab ] + 3ab.

→ [ (6)² - 2(4) / 4 ] + 2 [ 6/4] + 3(4).

→ [ 36 - 8 / 4 ] + [ 12/4 ] + 12.

→ [ 28/4 ] + 3 + 12.

→ 7 + 3 + 12 = 22.

Answer 2

Answer:

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