Equation

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Saumyojit

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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) ???
 
Mr. Bland said:
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.
Click to expand...
It needs to be minimised to a/d .
How can I bring it without using k .
 
I see......I was taught that formula differently.
So you want a compressed answer in variable terms?
 
firemath said:
I see......I was taught that formula differently.
So you want a compressed answer in variable terms?
Click to expand...

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) ?
 
Saumyojit said:
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) ???
Click to expand...

Why not use the k method, which seems simplest?

I think you mean, not "minimize" (which means, find the lowest value of), but "simplify".

Saumyojit said:
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) ?
Click to expand...
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.
 
Dr.Peterson said:
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.
Click to expand...

I have substituted c = b^2/a, d = c^2/b = b^3/a^2 .
but i am stuck after 2 steps and i cannot further minimize it .
Please show me the whole steps using this method : c = b^2/a, d = c^2/b = b^3/a^2
 
Please show your work, so I can see where you are stuck! I want to help you learn to get yourself unstuck.
 
(b^3 + c^3 + d^3)/(a^3+b^3+c^3) =(abc +bdc+d^3)/(a^3+abc+bdc)=then what?

b^3=abc

c^3=bdc
 
That's not the substitution I suggested. Why did you say, "I have substituted c = b^2/a, d = c^2/b = b^3/a^2"? You didn't.

The idea is to express everything in terms of a and b only, so that you can simplify the expression. For example, c^3 will become (b^2/a)^3 = b^6/a^3, and d^3 will become (b^3/a^2)^3 = b^9/a^6. You'll have a complex fraction that you can simplify by multiplying numerator and denominator by the LCD.
 
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??
 
Then, since the parenthesized factors in numerator and denominator look so similar, you should check your work to see if maybe they are really identical and can be cancelled!
 
Please do as I said, and check your work on factoring the numerator. Is it really true that

{b^3+b^6/a^3 +b^9/a^6 } = {b^3 *a^6 +b^3*a^3+b^9}/a^6 ?​

A major part of doing mathematics well is to learn to check your work and catch errors.
 
Saumyojit said:
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??
Click to expand...
Did you REVIEW your work and are you certain that above expression is correct?
 
@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.
 
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