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1.

If (5a+3b) is proportional to (9a+8b), Then prove that (a³+b³) is proportional to (a³-b³).

Answer» Given

(5a+3b) prop (9a+8b)

=>5a+3b=k(9a+8b),where k is constant

=>a(5a-9k)=b(8k-3)

=> a/b=(8k-3)/(5a-9k)= a constant =m (say)

So a=mb

Now

(a^3+b^3)/(a^3-b^3)

=(m^3b^3+b^3)/(m^3b^3-b^3)

=(m^3+1)/(m^3-1)= a constant

Hence

(a^3+b^3) prop (a^3-b^3)
Discussion