If a-b = 7 , a2 + b2 = 85, find a3 - b3 ?

Asked by nisha_vini29 | 4th Jul, 2017, 10:03: AM

Expert Answer:

begin mathsize 16px style straight a minus straight b equals 7
rightwards double arrow left parenthesis straight a minus straight b right parenthesis squared equals 7 squared
rightwards double arrow straight a squared plus straight b squared minus 2 ab equals 49
rightwards double arrow left parenthesis straight a squared plus straight b squared right parenthesis minus 2 ab equals 49
rightwards double arrow 85 minus 2 ab equals 49
rightwards double arrow 2 ab equals 36
rightwards double arrow ab equals 18
Now comma
straight a cubed minus straight b cubed equals left parenthesis straight a minus straight b right parenthesis cubed plus 3 ab left parenthesis straight a minus straight b right parenthesis
space space space space space space space space space space space space equals left parenthesis 7 right parenthesis cubed plus 3 cross times 18 cross times 7
space space space space space space space space space space space space equals 343 plus 378
space space space space space space space space space space space space equals 721
end style

Answered by Rashmi Khot | 4th Jul, 2017, 11:22: AM