#968 · Algebra · Sequences & series

Four proportionals with given sums

Find four numbers $a, b, c, d$ in continued proportion (so $\frac{a}{b} = \frac{b}{c} = \frac{c}{d}$ ) such that $a + d = 21$ , $b + c = 19$ , and $a^{2} + b^{2} + c^{2} + d^{2} = 442$ .

~5 minAnswer checked instantlyproportionsystems of equations

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. II. Proportion, Examples II, No. 19

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).