a-b-c-d-a-3-b-3-625-c-3-d-3-1-Find-a-b-c-d-

Question Number 207394 by hardmath last updated on 13/May/24

\frac{a}{b} = \frac{c}{d}

a^{3} - b^{3} = 625

c^{3} - d^{3} = 1

Find : a, b, c, d = ?

Answered by mr W last updated on 13/May/24

\frac{a}{b} = \frac{c}{d} = k, s a y

a = k b, c = k d w i t h k \neq 1

b^{3} (k^{3} - 1) = 625 \Rightarrow b = \sqrt[3]{\frac{625}{k^{3} - 1}} \Rightarrow a = k \sqrt[3]{\frac{625}{k^{3} - 1}}

d^{3} (k^{3} - 1) = 1 \Rightarrow d = \frac{1}{\sqrt[3]{k^{3} - 1}} \Rightarrow c = \frac{k}{\sqrt[3]{k^{3} - 1}}

3 e q u a t i o n s f o r 4 v a r i a b l e s, s o

t h e r e i s n o u n i q u e s o l u t i o n .

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