Question

4. Without actual calculating the cubes, find the value of each of the following (1) (-10)3 + (7)3 + (3)° - 34207943 Gry (28) + (-15) + (-13) 3 5 (iv) (0.2)2-(0.3)3 + (0.1)3 3 6​

Answer 1

i) (-12)³ + (7)³ + (5)³

Let x = -12, y = 7, z = 5

Then x + y + z = -12 + 7 + 5 = 0

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

Thus, (-12)³ + (7)³ + (5)³ = 3(-12)(7)(5)

= -1260

ii) (28)³ + (-15)³ + (-13)³

Let x = 28, y = -15, z = -13

Then x + y + z = 28 - 15 - 13 = 0

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

Thus, (28)³ + (-15)³ + (-13)³ = 3(28)(-15)(-13)

= 16380

HOPE IT HELPS U :D