{"id":265577,"date":"2025-07-22T07:40:30","date_gmt":"2025-07-22T07:40:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=265577"},"modified":"2025-07-22T07:40:33","modified_gmt":"2025-07-22T07:40:33","slug":"the-difference-between-a-number-and-its-reciprocal-is-3-2-find-the-number","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/22\/the-difference-between-a-number-and-its-reciprocal-is-3-2-find-the-number\/","title":{"rendered":"The difference between a number and its reciprocal is 3\/2 find the number"},"content":{"rendered":"\n

The difference between a number and its reciprocal is 3\/2 find the number<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let’s define the number as x<\/strong>.<\/p>\n\n\n\n

The reciprocal of x<\/strong> is 1\/x<\/strong>. According to the problem, the difference between a number and its reciprocal is 3\/2<\/strong>. Therefore, the equation can be written as:x\u22121x=32x – \\frac{1}{x} = \\frac{3}{2}x\u2212x1\u200b=23\u200b<\/p>\n\n\n\n

To solve for x<\/strong>, first multiply both sides of the equation by x<\/strong> to eliminate the denominator:x2\u22121=32xx^2 – 1 = \\frac{3}{2} xx2\u22121=23\u200bx<\/p>\n\n\n\n

Next, multiply the entire equation by 2 to get rid of the fraction:2×2\u22122=3x2x^2 – 2 = 3x2x2\u22122=3x<\/p>\n\n\n\n

Now, move all terms to one side to set the equation to zero:2×2\u22123x\u22122=02x^2 – 3x – 2 = 02×2\u22123x\u22122=0<\/p>\n\n\n\n

This is a quadratic equation. We can solve it using the quadratic formula, which is:x=\u2212b\u00b1b2\u22124ac2ax = \\frac{-b \\pm \\sqrt{b^2 – 4ac}}{2a}x=2a\u2212b\u00b1b2\u22124ac\u200b\u200b<\/p>\n\n\n\n

For our equation 2×2\u22123x\u22122=02x^2 – 3x – 2 = 02×2\u22123x\u22122=0, the coefficients are:<\/p>\n\n\n\n