Question 22
SSC-CGL 2020 Mar 3 Shift 1
If x⁴ + x²y² + y⁴ = 21, x² + xy + y² = 7, then the value of (1/x² + 1/y²) = ?
Solution in Brief
Factorize x⁴ + x²y² + y⁴ = (x² + xy + y²)(x² - xy + y²), to get x² - xy + y² = 3. Subtract it from x² + xy + y² = 7 to get xy = 2. Make a guess x = 1, y = 2 to get 5/4 as the answer!
Solution in Detail
Given
Also given
Add to both sides:
Completing the squares
Putting from (1),
Put in (1),
To find
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