Question

(If a a - 1/a = 5 , prove that a ^ 3 - 1/(a ^ 3) = 140
​with process please

Answer 1

`a-(1)/(a) =5\\(a)x^(3) -y^(3) =(x-y)(x^(2) +y^(2) +xy)\\(b)x^(2) +y^(2) =(x-y)^(2) +2xy\\a^(3) -(1)/(a^(3))=\\ a^(3) -((1)/(a))^(3) = //use(a)\\(a -(1)/(a))(a^(2) +((1)/(a) )^(2) +a*(1)/(a))=\\(a -(1)/(a))(a^(2) +((1)/(a) )^(2) +1)= //use(b)\\(a -(1)/(a))[(a-(1)/(a) )^(2) +2*a*(1)/(a) +1]=\\ \\5*[5^(2) +2+1]=5*28=140`Answer:

Explanation: