Among 3 4 , 4 5 and 12 10 which one is the smallest ?

Given that, 3 4 , 4 5 and 12 10 To find : which one is the smallest Now, The order of given surds are 4 , 5 , 10 respectively. ∴ LCM of 4 , 5 , 10 = 20 So, 3 4 = 3 5 20 = 243 20 4 5 = 4 4 20 = 256 20 12 10 = 12 2 20 = 144 20 Clearly, 144 20 > 243 20 > 144 20 Or, 12 10 > 3 4 > 4 5 Hence, 12 10 is the smallest.

Between 5 + 4 and 6 + 3 which one is greater?

Given that, 5 + 4 and 6 + 3 To find : which one is greater? Now, We know that, 3 = 1 . 72 , 4 = 2 5 = 2 . 23 , 6 = 2 . 44 So, substituting the above values in both the given equations, we get 5 + 4 = 2 + 2 . 23 = 4 . 23 And 6 + 3 = 2 . 44 + 1 . 72 = 4 . 16 Hence, 5 + 4 is greater.

x - 1 x = 2 3 , then what is the value of x + 1 x ?

Given that, x - 1 x = 2 3 To find : the value of x + 1 x Now, x - 1 x = 2 3 x - 1 x 2 = 2 3 2 x 2 + 1 x 2 - 2 × x × 1 2 = 12 x 2 + 1 x 2 - 2 = 12 x 2 + 1 x 2 = 14 Let x + 1 x = y Squaring both side x + 1 x 2 = y 2 x 2 + 1 x 2 + 2 = y 2 14 + 2 = y 2 16 = y 2 y = ± 16 y = ± 4 . Hence, this is the required answer.

If x = 2 + 3 + 5 and y = 2 + 3 - 5 show that, x - y 2 = 20 .

Given that, x = 2 + 3 + 5 and y = 2 + 3 - 5 To show : x - y 2 = 20 Now, x - y 2 = 20 2 + 3 + 5 - 2 + 3 - 5 2 = 20 Using a - b 2 = a 2 + b 2 - 2 ab 2 + 3 + 5 2 + 2 + 3 - 5 2 - 2 2 + 3 + 5 2 + 3 - 5 = 20 = 20 L.H.S=R.H.S Hence, this is the required answer.

The expression which is subtracted from 125 to give 5 is i 80 ii 100 iii 120 which one is correct?

Given that, The expression which is subtracted from 125 to give 5 is i 80 ii 100 iii 120 To find : which one is correct Now, 125 - 5 = 5 5 - 5 = 4 5 = 16 × 5 = 80 Hence, this is the required option.