Find c, if 4 ${a b}^{2}$ , 5 $a^{2} b$ and c are in continued proportion.

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Solution

Continued proportion means

$4 a b^{2} : 5 a^{2} b = 5 a^{2} b : c$

$\frac{4 a b^{2}}{5 a^{2} b} = \frac{5 a^{2} b}{c}$

$\frac{4 b}{5 a} = \frac{5 a^{2} b}{c}$

$c = \frac{5 a^{2} \times 5 a}{4} = \frac{25 a^{3}}{4}$

$c = \frac{25 a^{3}}{4}$ .

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a = 6

c = 24

If $x^{2}$ , 4 and 9 are in continued proportion, find x.

If a, b, and c are in continued proportion, then $a \times c = b^{2}$ .

A = a^{2} b + a b^{2} - a^{2} c - a c^{2},

B = b^{2} c + b c^{2} - a^{2} b - a b^{2}

C = a^{2} c + a c^{2} - b^{2} c - b c^{2}

a > b > c > 0

A x^{2} + B x + C = 0

a, b, c

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