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SSC CGL 2021 PYQ — Question 75

SSC CGL - 24 Aug 2021 - Shift 1 • Quantitative Aptitude • Q75

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If a4 + b4 + a2b2 = 273 and a2 + b2 - ab = 21, then one of the values of is :

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Correct answer: B

Explanation

The correct answer is option 2 i.e.  - 34\frac{3}{4} 

a4 + b4 + a2b2 = 273,

(a2)2 + (b2)2 + 2 a2b2 - a2b2 = 273

(a2 + b2)2 = 273 + a2b2 ..............(1)

a2 + b2 - ab = 21

a2 + b2 = 21 + ab ......................(2)

On putting the value of eq 2 in eq 1 we get,

441 + a2b2 + 42ab = 273 + a2b2 

42ab = 273 - 441

ab = -4.........................(3)

a2 + b2 - ab = 21

on adding 2ab on both sides we get,

a2 + b2 + 2ab = 21 + 3ab

(a + b)2 = 21 + 3 × -4 = 9

a + b = +3 and -3.

If a + b = +3 then 1/a + 1/b = -3/4.

If a + b = -3 then 1/a + 1/b = -3/-4 = 3/4.