Ratio and Proportion — Mathematics STD 10 — Question
ICSE BoardEnglish MediumSTD 10MathematicsRatio and Proportion2 Marks
Question
Find the mean proportional between $6+3 \sqrt{3}$ and $8-4 \sqrt{3}$
✓
Answer
Let the mean proportional between $6 + 3\sqrt3$ and $8 – 4\sqrt3 be x.\Rightarrow 6 + 3\sqrt3, x$ and $8 – 4\sqrt3$ are in continued proportion.
$\Rightarrow 6 + 3\sqrt3 : x = x : 8 – 4\sqrt3$
$\Rightarrow x \times x = (6 + 3\sqrt3) (8 – 4\sqrt3)$
$\Rightarrow x^2= 48 + 24\sqrt3- 24\sqrt3 – 36$
$\Rightarrow x^2= 12$
$\Rightarrow x = 2\sqrt3$
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