Mathematics

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
Correct Answer: Option C
Explanation

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})