Question

If 3a-2b+5c=5 and 6ab+10bc-15ac=14, find the value of 27a3+125c3+90abc-8b3.

Answer 1

3a-2b+5c=5
Cubing both sides,
{(3a-2b)+5c}³=5³
or, (3a-2b)³+3.(3a-2b)².5c+3(3a-2b).(5c)²+125c³=125
or, 27a³-3.9a².2b+3.3a.4b²-8b³+3.(9a²-2.3a.2b+4b²).5c+(9a-6b)(25c²)+  125c³=125
or, 27a³-54a²b+36ab²-8b³+(27a²-36ab+12b²).5c+225ac²-150bc²+125c³=125
or, 27a³-54a²b+36ab²-8b³+135a²c-180abc+60b²c+225ac²-150bc²+125c³=125
or, 27a³-8b³+125c³-54a²b-90abc+135a²c+36ab²+60b²c-90abc-90abc-150bc²+225ac²+90abc=125
or, 27a³-8b³+125c³-9a(6ab+10bc-15ac)+6b(6ab+10bc-15ac)-15c(6ab+10bc-15ac)+90abc=125
or, 27a³+125c³-8b³+90abc-9a×14+6b×14-15c×14=125 
[∵, 6ab+10bc-15ac=14]
or, 27a³+125c³+90abc-8b³-126a+84b-210c=125
or, 27a³+125c³+90abc-8b³-42(3a-2b+5c)=125
or, 27a³+125c³+90abc-8b³-42×5=125 [∵, 3a-2b+5c=5]
or, 27a³+125c³+90abc-8b³-210=125
or, 27a³+125c³+90abc-8b³=125+210
or, 27a³+125c³+90abc-8b³=335

Answer 2

Answer:

Answer is 335

You to cube on both the sides