Share

The Sum of a Number and Its Reciprocal is 17/4. Find the Number. - Mathematics

Course

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(𝑥2 + 1) = 17𝑥

⇒ 4𝑥2 - 17𝑥 + 4 = 0

⇒ 4𝑥2 - 16𝑥 - 𝑥 + 4 = 0

⇒ 4𝑥(𝑥 - 4) - 1(𝑥 - 4) = 0

⇒ 𝑥 =1/4 𝑜𝑟 𝑥 = 4

∴ The value of 𝑥 = 4

Is there an error in this question or solution?