Question

Evaluate :
(i) 25³ – 75³ + 50³
(ii) 48³ – 30³ - 18³
(iii) (½)³ + (⅓)³ - (⅚)³
(iv) (0.2)³ – (0.3)³+ (0.1)³

Answer 1

Step-by-step explanation:

(I) 25³- 75³ + 50³

=> 15625 - 421875 + 125000

= ( - 281250)

(II) 48³ - 30³ - 18³

=> 110592 - 27000 - 5832

= 77760

(III) (½)³ + (⅓)³ - (⅚)³

=> 1/8 + 1/27 - 125/216

= (27 + 8)/216 - 125/216

= 35/216 - 125/216

= (35-125)/216

= -90/216

:-- = -5/12

(IV) (0.2)³-(0.3)³+(0.1)³

=> 0.008 - 0.027 + 0.001

= -0.018

Answer 2

(i)  Given : 25³ – 75³ + 50³

 Let x = 25, y = - 75 & z = 50

x + y + z = 25 +( -75) + 50 = 0

Here, x + y + z = 0

We know that if,   x + y + z = 0, then x³ + y³ + z³ = 3xyz

(25)³ + (-75)³ + (50)³ = 3(25)(-75)(50) = - 281250

(25)³ + (-75)³ + (50)³ =  - 281250

(ii)  Given : 48³ – 30³ - 18³

Let x = 48, y = - 30 & z = -18

x + y + z = 48 +( -30) + (-18) = 0

Here, x + y + z = 0

We know that if,  x + y + z = 0, then x³ + y³ + z³ = 3xyz

(48)³ + (-30)³ + (-18)³ = 3(48) (-30) (-18) = 77760

(48)³ + (-30)³ + (-18)³ =  77760

(iii)  Given : (½)³ + (⅓)³ - (⅚)³

Let x = ½ , y = ⅓  & z = - ⅚  

x + y + z = ½  +(⅓ ) + (-⅚ ) = ⅚ - ⅚ = 0

Here, x + y + z = 0

We know that if,   x + y + z = 0, then x³ + y³ + z³ = 3xyz

(½ )³ + (⅓ )³ + (-⅚ )³ = 3(½ )(⅓ )(-⅚ ) = - 5/12

(½ )³ + (⅓ )³ + (-⅚ )³ = - 5/12

(iv) Given : (0.2)³ – (0.3)³ + (0.1)³

Let x = 0.2, y = - 0.3 & z = 0.1

x + y + z = 0.2 + ( - 0.3) + 0.1 = 0

Here, x + y + z = 0

We know that if,  x + y + z = 0, then x³ + y³ + z³ = 3xyz

(0.2)³ + (- 0.3)³ + (0.1)³ = 3(0.2)(- 0.3)(0.1) = - 0.018

(0.2)³ + (- 0.3)³ + (0.1)³ = - 0.018

 HOPE THIS ANSWER WILL HELP YOU…..

 

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