Question

if a2 + b2/ab = 25/12 then a3+b3/a3-b3=​

Answer 1

Step-by-step explanation:

a2 + b2/ab = 25/12

(a2 + b2+2ab-2ab)/ab = 25/12

((a+b)^2/ab ) -2=25/12

(a+b)^2/ab=25/12 +2

=(25+24)/12

=49/12

(a+b)^2=(49/12)ab

a+b=root(49/12 ab)

a+b=7root(ab/12)

(a2 + b2-2ab+2ab)/ab = 25/12

((a-b)^2/ab ) +2=25/12

(a-b)^2/ab=25/12 -2

=(25-24)/12

=1/12

(a-b)^2=(1/12)ab

a-b=root(1/12 ab)

=root(ab/12)

a3+b3/a3-b3=((a+b)^3-3ab(a+b)) / ((a-b)^3+3ab(a-b))

=(a+b)((a+b)^2-3ab)/(a-b)((a-b)^2+3ab)

=(7root(ab/12))(49/12 ab -3ab) / (root(ab/12))(1/12 ab + 3ab)

=(7(49ab-36ab)/12) / ((ab+36ab)/12)

=7(13ab)/(37ab)

=91/37