Question

if a minus b = 4 and a b equal 45 then find the value of a cube minus b cube

Answer 1

here is ur answer user:-

${a}^{3} - {b}^{3} = {(a - b)}^{3} + 3ab(a - b) \\ = {4}^{3} + 3 \times 45 \times 4 \\ = 64 + 540 \\ = 604 \: ans$

Answer 2

given :a-b=4--->(1),ab=45-----(2)
a-b=4==>a=4+b
from(2),,
(4+b)b=45
4b+b^2=45
b^2+4b-45=0
b=-4 +r- √16+180 / 2
=-4 +r- √196 / 2
=-4 +r- 14 / 2
=-4+14/2 and -4-14/2
b=5 ,-9
then b=5---(3)
from(2),
a(5)=45
a=9

then, a^3-b^3=9^3-5^3
=729-125=604

ANOTHER METHOD,,,

a^3-b^3=(a-b) (a^2+ab+b^2)
=4(81+45+25)
=4(151)
=604