It needs to be minimised to a/d .What exactly is it that needs to be solved? a, b, c and d can be solved using only the proportions, and the other expression isn't an equation.
most of the people would solve it using a/b = b/c=c/d = kI don't see a k.......
I see......I was taught that formula differently.
So you want a compressed answer in variable terms?
IF a/b = b/c=c/d then solve (b^3 + c^3 + d^3)/(a^3+b^3+c^3)
I dont want an approach using k.
I have started like this :
a/b = b/c =>
ac=b^2
b/c=c/d => bd =c^2
How will i minimize (b^3 + c^3 + d^3)/(a^3+b^3+c^3) ???
One way is to express c and d in terms of a and b: c = b^2/a, d = c^2/b = b^3/a^2. Make those substitutions, and simplify.see i know that
ac=b^2
b/c=c/d => bd =c^2
how will i substitute
ac=b^2
bd =c^2 in (b^3 + c^3 + d^3)/(a^3+b^3+c^3) ?
Why not use the k method, which seems simplest?
I think you mean, not "minimize" (which means, find the lowest value of), but "simplify".
One way is to express c and d in terms of a and b: c = b^2/a, d = c^2/b = b^3/a^2. Make those substitutions, and simplify.
Using a/b = b/c = c/d = k (or, as I prefer, b/a = c/b = d/c = k) is a lot less complicated.
Did you REVIEW your work and are you certain that above expression is correct?USING UR METHOD :
(b^3 + c^3 + d^3)/(a^3+b^3+c^3) = {b^3+b^6/a^3 +b^9/a^6 }/{a^3+b^3+b^6/a^3)}
=> {b^3 *a^6 +b^3*a^3+b^9}/a^6 * a^3 / {a^6+a^3 * b^3 + b^6} =>( b^3 *a^6 +b^3*a^3+b^9)/(a^6+a^3 * b^3+ b^6) * 1/a^3
after doing lcm
=>b^3 (a^6 +a^3+b^6)/a^3(a^6+a^3 * b^3+ b^6) then what??
it is compelted .@Saumyojit: To encourage you to continue, I will add that there is just one number wrong, and after fixing it you will be almost finished.