Find the third proportional to - i 22-3 and 4 ii a - b and a2 - b2

(i) Let the third proportional to 8/3 and 4 be x. ⟹8/3 , 4, x are in continued proportion. ⟹ 8/3 : 4 = 4 : x ⟹ 8/3/4 : 4/x ⟹x = 16×3/8=6 (ii) Let the third pr ...

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Standard X

Mathematics

Proportion

Find the thir...

Question

Find the third proportional to :

(i) $2 \frac{2}{3}$ and 4

(ii) a - b and $a^{2} - b^{2}$

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Solution

(i) Let the third proportional to $\frac{8}{3}$
and 4 be x.
⟹ $\frac{8}{3}, 4, x$ are in continued proportion.
⟹ $\frac{8}{3} : 4 = 4 : x$
⟹ $\frac{\frac{8}{3}}{4}$ : $\frac{4}{x}$
⟹ $x = 16 \times \frac{3}{8} = 6$

(ii) Let the third proportional to a − b and $a^{2} - b^{2}$
be x.
⟹ $a - b, a^{2} - b^{2}$ and x are in continued proportion.
⟹ $a - b : a^{2} - b^{2} = a^{2} - b^{2} : x$
⟹ $\frac{(a - b)}{(a^{2} - b^{2})} = \frac{(a^{2} - b^{2})}{x}$
⟹x= $\frac{(a^{2} - b^{2})^{2}}{(a - b)}$
⟹x= $\frac{(a + b) (a - b) (a^{2} - b^{2})}{(a - b)}$
⟹x = $(a + b) (a^{2} - b^{2})$

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Find the third proportional to : (i) 223 and 4 (ii) a - b and a2−b2

Find the third proportional to :

(i) $2 \frac{2}{3}$ and 4

(ii) a - b and $a^{2} - b^{2}$