1.

If 2x2 - 7x + 5 = 0, then what is the value of \(x^2 + \frac{25}{4x^2}\)?1. \(5 \frac{1}{2}\)2. \(7 \frac{1}{4}\)3. \(9 \frac{3}{4}\)4. \(9 \frac{1}{2}\)

Answer» Correct Answer - Option 2 : \(7 \frac{1}{4}\)

Concept used:

(a + b)2 = a2 + b2 + 2ab 

Calculations:

2x2 – 7x + 5 = 0

⇒ 2x2 + 5 = 7x

⇒ x2 + 5/2 = 7x/2

⇒ x + 5/2x = 7/2 

Square of both side of equation

⇒ (x + 5/2x)2 = (7/2)2 

⇒ x2 + (5/2x)2 + 2 × x × 5/2x = 49/4 

⇒ x2 + 25/4x2 + 5 = 49/4 

⇒ x2 + 25/4x2 = 49/4 – 5 

⇒ x2 + 25/4x2 = 29/4 

⇒ x2 + 25/4x2 = \(7 \frac{1}{4}\)

∴ The correct of answer is \(7 \frac{1}{4}\)


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