Ratio and Proportion — Mathematics STD 10 — Question
ICSE BoardEnglish MediumSTD 10MathematicsRatio and Proportion2 Marks
Question
If a, b, and c are in continued proportion, prove that $\frac{a^2+a b+b^2}{b^2+b c+c^2}=\frac{a}{c}$
✓
Answer
Given, a, b and c are in continued proportion.
Therefore,
$\frac{a}{b}=\frac{b}{c}$
$ac = b ^2$
Here,
$\frac{a^2+a b+b^2}{b^2+b c+c^2}$
$=\frac{a^2+a b+a c}{a c+b c+c^2}$
$ =\frac{a(a+b+c)}{c(a+b+c)} $
$ =\frac{a}{c}$
Hence proved.
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