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Find the product xy if, x, 3/2, 6/7, y are in G.P
...

Find the product xy if, x, 3/2, 6/7, y are in G.P

A.

24/49

B.

4/7

C.

9/7

D.

7/4

E.

21/8

View answer & explanation

Correct answer is C

In GP, when you are given three consecutive terms, say f, g, h, then

$f \times h = g^2$

Given: $x, \frac{3}{2}, \frac{6}{7}, y$ , then

$\frac{6x}{7} = (\frac{3}{2})^2 \implies \frac{6x}{7} = \frac{9}{4} ... (i)$

Also, $\frac{3y}{2} = (\frac{6}{7})^2 \implies \frac{3y}{2} = \frac{36}{49} ... (ii)$

From $\frac{6x}{7} = \frac{9}{4} \implies x = \frac{9 \times 7}{6 \times 4}$

$x = \frac{21}{8}$

Also, $\frac{3y}{2} = \frac{36}{49} \implies y = \frac{2 \times 36}{3 \times 49}$

= $\frac{24}{49}$

$xy = \frac{21}{8} \times \frac{24}{49} = \frac{9}{7}$

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