If a, b and c are in continued proportion, then prove that : 3a^2 + 5ab + 7b^2/3b^2 + 5bc + 7c^2 = a/c .

Since, a, b and c are in continued proportion. Substituting, b2 = ac in L.H.S. of equation , we get : Hence, proved that .

Mathematics

If a, b and c are in continued proportion, then prove that :
$\dfrac{3a^2 + 5ab + 7b^2}{3b^2 + 5bc + 7c^2} = \dfrac{a}{c}$ .

Ratio Proportion

ICSE Sp 2024

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Answer

Since, a, b and c are in continued proportion.

$\therefore \dfrac{a}{b} = \dfrac{b}{c} \\[1em] \Rightarrow b^2 = ac.$

Substituting, b² = ac in L.H.S. of equation $\dfrac{3a^2 + 5ab + 7b^2}{3b^2 + 5bc + 7c^2} = \dfrac{a}{c}$ , we get :

$\Rightarrow \dfrac{3a^2 + 5ab + 7ac}{3ac + 5bc + 7c^2} \\[1em] \Rightarrow \dfrac{a(3a + 5b + 7c)}{c(3a + 5b + 7c)} \\[1em] \Rightarrow \dfrac{a}{c}.$

Hence, proved that $\dfrac{3a^2 + 5ab + 7b^2}{3b^2 + 5bc + 7c^2} = \dfrac{a}{c}$ .

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Mathematics

If a, b and c are in continued proportion, then prove that :
$\dfrac{3a^2 + 5ab + 7b^2}{3b^2 + 5bc + 7c^2} = \dfrac{a}{c}$ .

Ratio Proportion

ICSE Sp 2024

Answer

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If a, b and c are in continued proportion, then prove that :3a2+5ab+7b23b2+5bc+7c2=ac\dfrac{3a^2 + 5ab + 7b^2}{3b^2 + 5bc + 7c^2} = \dfrac{a}{c}3b2+5bc+7c23a2+5ab+7b2​=ca​.

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ICSE Sp 2024

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In a recurring deposit account for 2 years, the total amount deposited by a person is ₹ 9600. If the interest earned by him is one-twelfth of his total deposit, then find :(a) the interest he earns(b) his monthly deposit(c) the rate of interest

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If a, b and c are in continued proportion, then prove that :
$\dfrac{3a^2 + 5ab + 7b^2}{3b^2 + 5bc + 7c^2} = \dfrac{a}{c}$ .

In a recurring deposit account for 2 years, the total amount deposited by a person is ₹ 9600. If the interest earned by him is one-twelfth of his total deposit, then find :
(a) the interest he earns
(b) his monthly deposit
(c) the rate of interest

Find :
(a) (sin θ + cosec θ)²
(b) (cos θ + sec θ)²
Using the above results prove the following trigonometry identity :
(sin θ + cosec θ)² + (cos θ + sec θ)² = 7 + tan² θ + cot² θ

Study the graph and answer each of the following :
(a) Name the curve plotted
(b) Total number of students
(c) The median marks
(d) Number of students scoring between 50 and 80 marks.