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The quotient of a reciprocal would equal the numerator squared divided by the denominator squared. i.e. (x/y)/(y/x) = x2/y2
Number x Reciprocal = 1 Therefore Reciprocal = 1/Number
Any number multiplied by its reciprocal is equal to ' 1 '.
Let's call the number x, then the reciprocal is 1/x 3/x is three times the reciprocal and that equals two. So 3/x=2 or3=2x and means x=3/2 Check it x=3/2 reciprocal is 2/3 and 3x 2/3=2.
A number . . . ' x 'Its reciprocal . . . 1/xTwice its reciprocal . . . 2/xThe sum of (the number) and (twice its reciprocal) . . . x + 2/xThe equation:x + 2/x = 3Multiply each side of the equation by 'x' :x2 + 2 = 3xSubtract 3x from each side:x2 - 3x + 2 = 0Factor the left side, in order to see what's going on:(x - 1) (x - 2) = 0This is true if 'x' is either ' 1 ' or ' 2 '.x = 1The sum of the number and twice its reciprocal . . . 1 + 2/1 = 3X = 2The sum of the number and twice its reciprocal . . . 2 + 2/2 = 3