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Question
The sum of a number and its reciprocal is 17/4. Find the number.
Solution
Let the number be ‘x’
According to the given hypothesis
`x+1/x=17/4`
`rArr(x^2+1)/x=17/4`
⇒ 4(๐ฅ2 + 1) = 17๐ฅ
⇒ 4๐ฅ2 - 17๐ฅ + 4 = 0
⇒ 4๐ฅ2 - 16๐ฅ - ๐ฅ + 4 = 0
⇒ 4๐ฅ(๐ฅ - 4) - 1(๐ฅ - 4) = 0
⇒ ๐ฅ =1/4 ๐๐ ๐ฅ = 4
∴ The value of ๐ฅ = 4
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