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Compound Ratio

What is the c...

Question

What is the compounded ratio of $(a - b) : (a + b), (a - b)^{2} : (a + b)^{2}$ and $(a + b)^{3} : (a - b)^{3}$

8 : 9

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5 : 7

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1 : 1

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3 : 5

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Solution

The correct option is C $1 : 1$
By the defination of compound ratio these ratio can be expressed as
$\frac{a - b}{a + b} \times \frac{(a - b)^{2}}{(a + b)^{2}} \times \frac{(a + b)^{3}}{(a - b)^{3}} = \frac{1}{1}$
Hence, $1 : 1$ .

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Similar questions

(a + b)^{2}

(a - b)^{2}

(a^{2} + b^{2})

(a + b)^{3}

(a - b)^{3}

a^{3} + b^{3}

a^{3} - b^{3}

(a + b) : (a - b) = 1 : 5

(a^{2} - b^{2}) : (a^{2} + b^{2}) .

x = 1 + a + a^{2} + a^{3} + . . . .

\infty (| a | < 1)

y = 1 + b + b^{2} + b^{3} + . . .

\infty (| b | < 1)

1 + a b + a^{2} b^{2} + a^{3} b^{3} + . . .

\infty = \frac{x y}{x + y - 1}

a + b = 5

a^{2} + b^{2} = 11

a^{3} + b^{3} = 20

(i) (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)

(i i) (a + b)^{3} = a^{3} + b^{3} + 3 a b (a - b)

(i i i) (a - b)^{3} = a^{3} - b^{3} - 3 a b (a + b)

(i v) a^{2} - b^{2} = (a + b) (a - b)

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