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Let The Number be x

According to Given Question

1 + x = 4.25

--

x

1 + x² = 425

-------- -------

x 100

100 + 100x² = 425x

100x² - 425x + 100 = 0

Dividing the Equation by 25

4x² - 17x + 4 = 0

4x² - 16x - x + 4 = 0

4x(x - 4) -1(x - 4) = 0

(4x - 1)(x - 4) = 0

According to Given Question

1 + x = 4.25

--

x

1 + x² = 425

-------- -------

x 100

100 + 100x² = 425x

100x² - 425x + 100 = 0

Dividing the Equation by 25

4x² - 17x + 4 = 0

4x² - 16x - x + 4 = 0

4x(x - 4) -1(x - 4) = 0

(4x - 1)(x - 4) = 0

**x = 1/4 OR x = 4**

So the Number is either 1/4 or 4

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So the Number is either 1/4 or 4

Mark This Brainliest If This Helped u

Number added to its reciprocal is 4.25

So, x + (1/x) = 4.25

⇒ x2 + 1 = (425/100)x

⇒ x2 + 1 = (17/4)x

⇒ 4x2 + 4 = 17x

⇒ 4x2 – 17x + 4 = 0

⇒ 4x2 – 16x – x + 4 = 0

⇒ 4x(x – 4) – 1( x – 4) = 0

⇒ (x – 4)(4x – 1) = 0

⇒ (x – 4) = 0 or (4x – 1) = 0

∴ x = 4 or (1/4)

**Thus the number is 4 or (1/4).**