Question

U by the square method. 39. Ifa, ß are the roots of the equation 2x2-3x - 4 = 0 form the equation whose root are 1/a²,1/ ß²
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Answer 1

Answer:

Step-by-step explanation:

Given equation : 2x² - 3x - 4 = 0.

By comparing with ax²+ bx +c = 0 ,we have

a = 2 , b = - 3 and c = - 4.

D = b² - 4ac = ( - 3 )² - 4 ( 2 ) ( - 4 ) = 9 + 32 = 41

∴ x = - b ± √b² - 4ac / 2a

= - ( - 3 ) ± √41 / (2 × 2 )

= 3 ± √41 / 4

∴ α = 3 - √41 / 4 and β = 3 + √41 / 4.

1 / α = 1 / (3 - √41/4)= 4 / (3 - √41 ) (∵ By rationalising the denominator )

= 4 / (3 - √41) × ( 3 + √41) / ( 3 + √41 )

= 4 (3 + √41 ) / ( 3)² - (√41)²

= 4 (3 + √41 ) / 9 - 41

= 4 (3 + √41) / ( - 32)

= -3 - √41 / 8

1 / α² = 1 / ( -3-√41 / 8)²= 1/ (9 + 41 + 6√41 /64)= 64 / ( 50 + 6√41 )

Same as

1/ β = 1 / (3+√41 / 4) = 4 / (3+√41) (∵By rationalising the denominator)

= 4 / (3+√41) × (3-√41) / (3-√41)

= 4 (3-√41) / ( 3 )² - ( √41)²

= 4 (3-√41) / ( 9 - 41)

= 4 (3 - √41 )/ (- 32)

= -3 + √41 / 8

1 / β² = 1 / ( -3+√41 / 8)² = 1 / ( 9+41 -6√41 / 64 ) = 64 / ( 50 - 6√41 )