Given that,
a = (?2 - 1)1/3
By cubing the both side of the given equation.
a3 = ?2 - 1
Then 1/a3 = 1/?2 - 1
Now multiply and divide the above equation by ?2 + 1
? 1/a3 = ( ?2 + 1 ) / ( ?2 + 1 ) x 1/(?2 - 1 )
? 1/a3 = ( ?2 + 1 ) x 1 / ( ?2 + 1 ) x (?2 - 1 ) [ Use the formula (A + B)(A - B) = A2 - B2 ]
? 1/a3 = ( ?2 + 1 ) / ( 2 - 1 )
? 1/a3 = ?2 + 1
According to the question
( a - a-1 )3 + 3 ( a - a-1 )
= (a - 1/a)3 + 3(a - 1/a) Use the formula [ ( A - B)3 = A3 - B3 + 3AB(A - B) ]
= a3 - 1/a3 - 3 a x 1/a (a -1/a) + 3(a - 1/a)
= a3 - 1/a3 - 3 (a -1/a) + 3(a - 1/a)
= a3 - 1/a3
Pu the value of a3 and 1/a3
= ?2 -1 - ( ?2 + 1 )
= ?2 -1 - ?2 - 1
= -2
We have the important relation, More work, More time (days)
? A piece of work can be done in 6 days.
? Three times of work of same type can be done in 6 x 3
= 18 days
? = 750.0003 ÷ 19.999
? ? ? 750 ÷ 20
? ? ? 375 ? 38
Subtract 20, 25, 30, 35, 40, 45 from successive numbers. So 0 is wrong.
NA
Each previous number is multiplied by 2.
? 8 m shadow means original height = 12 m
? 1 m shadow means original height = 12/8 m
? 100 m shadow means original height = (12/8) x 100 m
= (6/4) x 100 = 6 x 25 = 150 m
Let 8% of 96 = y of 1/25
? (8 x 96)/100 = y/25
? y = (8 x 96 x 25)/100 = 192
Since the principal is not given, so data is inadequate.
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