x + 1/x = 3 ........................ (i)
On squaring both side, we will get
(x + 1/x)2 = (3)2
Use the Square algebra formula (a + b)2 = a2 + 2ab + b2
? x2 + 1/x2 + 2 = 9
? x2 + 1/x2 = 7 ..................(ii)
Again squaring both sides, we will get
(x2 + 1/x2)2 = (7)2
Use the Square algebra formula (a + b)2 = a2 + 2ab + b2
? x4 + 1/4 + 2 = 49
? x4 + 1/x4 = 47 .....................(iii)
On cubing the equation (i) both side, we will get
(x + 1/x)3 = (3)3
Use the cube algebra formula (a + b)3 = a3 + 3a2b + 3ab2 + b3
? x3+ 1/x3 + 3(x + 1/x) = 27
? x3 + 1/x3 + 9 = 27 [? (x + 1/x) = 3]
? x3 + 1/x3 = 18 ...................(iv)
On multiplying Eqs. (i) and (iii) , we get
? (x4 + 1/x4) (x + 1/x) = 47 x 3
? x5 + 1/x5 + x3 + 1/x3 = 141
? x5 + 1/x5 + 18 = 141 [from Eq. (iv)]
? x5 + 1/x5 = 123
47/10000 = .0047
.02 =(2/100) x 100% =2%
Let N / 11 = 233
Then, N = 233 x 11 = 2563
? Missing digit is 5.
121012 = 12 x 10084 + 4
? remainder = 4
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.
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