1.

If ‘α’ and ‘β’ are the roots of expression x2 – 12x + 27 = 0, then find the value of 1/β2 – 1/α2.1. 10/812. 8/813. 4/94. 22/27

Answer» Correct Answer - Option 2 : 8/81

GIVEN:

‘α’ and ‘β’ are the roots of expression x2 – 12x + 27 = 0

FORMULA USED:

(α – β)2 = (α + β)2 – 4αβ

(α2 – β2) = (α – β)(α + β)

CALCULATION:

Since ‘α’ and ‘β’ are the roots of expression x2 – 12x + 27 = 0.

α + β = -b/a = 12      ---- (1)

αβ = c/a = 27      ---- (2)

From (1) and (2):

(α – β)2 = (α + β)2 – 4αβ

⇒ (α – β)2 = 144 – 108 = 36

⇒ α – β = 6

Now,

1/β2 – 1/α2

⇒ (α2 – β2)/α2β2

⇒ [(α – β)(α + β)]/α2β2

⇒ [(6 × 12)/272]

⇒ 8/81

∴  The value of 1/β2 – 1/α2 is 8/81.


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