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If x : y = 3 : 7, then 6x2 - 2xy + y2⁄xy is equal to
Explanation
Given the ratio x : y = 3 : 7, we can assume x = 3k and y = 7k for some constant k.
Substitute these values into the expression:
6x2 - 2xy + y2⁄xy
Numerator = 6(3k)2 - 2(3k)(7k) + (7k)2
= 6(9k2) - 42k2 + 49k2
= 54k2 - 42k2 + 49k2 = 61k2
Denominator = (3k)(7k) = 21k2
The value of the expression is 61k2⁄21k2 = 61⁄21.
Alternatively, the expression can be simplified by dividing the numerator and denominator by xy: 6(x/y) - 2 + (y/x). Substituting x/y = 3/7 and y/x = 7/3 gives: 6(3/7) - 2 + 7/3 = 18/7 - 2 + 7/3 = 4/7 + 7/3 = (12 + 49) / 21 = 61/21.
SIMILAR QUESTIONS
If X + 2Y = 2X + Y, then X^2 / Y^2 is equal to
If a and B are the roots of the equation x2- 7x + 11 = 0, then the value of x3 + p3 is equal to :
Suppose x is the smallest integer greater than 3 such that when it is divided by 6 or 8, the remainder is 3. y is the smallest integer greater than 2 such that when it is divided by 6 or 8, the remainder is 2. What is x - y ?
If * operation on the set of integers is defined as x * y = 2x + y- xy, then (3* 2)*(2*1) is :