# If x4 + x2y2 + y4 = 273 and x2 – xy + y2 = 13, then the value of xy is:

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## Options:

1. 6

2. 8

3. 10

4. 4

### Correct Answer: Option 4 (Solution Below)

This question was previously asked in

SSC CGL Previous Paper 72 (Held On: 5 March 2020 Shift 2)

## Solution:

Given:

x2 – xy + y2 = 13      ----(1)

x4 + x2y2 + y4 = 273

Formula used:

(x2 – xy + y2)(x2 + xy + y2) = x4 + x2y2 + y4

Calculation:

(x2 – xy + y2)(x2 + xy + y2) = x4 + x2y2 + y4

⇒ 13 × (x2 + xy + y2) = 273

⇒ (x2 + xy + y2) = 273/13 = 21      ----(2)

eq(2) - eq(1),

2xy = 8

⇒ xy = 4

∴ xy = 4
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