If three homogenous quantities a - b - c are in continued proportion such that a - b - b - c- then which of the following is true-A- b 2- acB- b - ac C- b2-acD- b-a-c

The correct options are A b^2=ac B b = ±√(ac) If three homogenous quantities a, b, c nbsp; are in continued proportion such that a/b = b/c or b^2 = ac, or b ...

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Standard X

Mathematics

Proportion

If three homo...

Question

If three homogenous quantities a, b, c are in continued proportion such that $\frac{a}{b} = \frac{b}{c}$ , then which of the following is true?

$b^{2} = a c$

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$b = \pm \sqrt{a c}$

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$b^{2} = a^{c}$

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b - a = c

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Solution

The correct options are
A
$b^{2} = a c$

B
$b = \pm \sqrt{a c}$

If three homogenous quantities a, b, c are in continued proportion such that $\frac{a}{b} = \frac{b}{c} o r b^{2} = a c$ , or $b = \pm \sqrt{a c}$ , then b is said to be the mean-proportional of a and c.

Hence, the above statement is true.

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Similar questions

If three homogeneous quantities a,b and c are in continued proportion, such that $\frac{a}{b} = \frac{b}{c} o r b^{2} = a c o r b = \pm \sqrt{a c}$ , then b is said to be the mean proportional of a and c

Q. If

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are in continued proportion, prove that

{(\frac{a - b}{c} + \frac{a - c}{b})}^{2} - {(\frac{d - b}{c} + \frac{d - c}{b})}^{2} = {(a - d)}^{2} (\frac{1}{c^{2}} + \frac{1}{b^{2}})

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b + c) = a² + b² + c². then show that a, b, c are in continued proportion.

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

Q. If (a + b + c) (a

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b + c) = a²+ b²+ c²show that a, b, c are in continued proportion.

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If three homogenous quantities a, b, c are in continued proportion such that ab=bc, then which of the following is true?

The correct options are A b2=ac B b=±√ac If three homogenous quantities a, b, c are in continued proportion such that ab=bc or b2=ac, or b=±√ac, then b is said to be the mean-proportional of a and c. Hence, the above statement is true.

If three homogenous quantities a, b, c are in continued proportion such that $\frac{a}{b} = \frac{b}{c}$ , then which of the following is true?