1.

If x - y = 13 and xy = 25, then the value of x2 - y2 = ?1. 13√2292. 13√2103. 13√2694. 13√240

Answer» Correct Answer - Option 3 : 13√269

Given:

x – y = 13

xy = 25

Formula Used:

(x – y)2 = x2 + y2 – 2xy

(x + y)2 = x2 + y2 + 2xy

x2 – y2 = (x – y) × (x + y)

Calculation:

x – y = 13

Squaring both the sides

⇒ (x – y)2 = 132

⇒ x2 + y2 – 2xy = 169

⇒ x2 + y2 = 169 + 2 × 25

⇒ x2 + y2 = 219

(x + y)2 = x2 + y2 + 2xy

⇒ (x + y)2 = 219 + 2 × 25

⇒ (x + y) = √(269)

x2 – y2 = (x – y) (x + y)

⇒ x2 – y2 = 13√269

∴ The value of x2 – y2 is 13√269.  


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