A non-zero number is greater than 7 times its reciprocal by 9.3. What is the number?
10
Step 1 - Set up: Let the number be \(x\). "Greater than 7 times its reciprocal by 9.3" gives:
\[x = \frac{7}{x} + 9.3\]
Step 2 - Clear the fraction (multiply by \(x\)):
\[x^2 - 9.3x - 7 = 0\]
Step 3 - Solve: Multiplying through by 10 gives \(10x^2 - 93x - 70 = 0\), which factorises as \((x-10)(10x+7)=0\). The positive root is \(x=10\).
Check: \(\tfrac{7}{10}+9.3 = 0.7+9.3 = 10\). Therefore the number is 10.
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