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SSC Selection Post 2022 PYQ — Question 72

SSC Selection Post - Matriculation Level - 3 Feb 2022 - Shift 1 • Quantitative Aptitude • Q72

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If a+b=34a+b= {{3} \over 4}, and ab=18ab= {{1} \over 8}, then the value of a4+b4+ab3+ba3{{a^4+b^4+ab^3 +ba^3}} is:

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Correct answer: C

Explanation

The correct answer is Option 3 i.e. 27256{{27} \over 256}.

a+b=34a+b= {{3} \over 4}

Square both sides

⇒ (a+b)2=(34)2(a+b)^2= ({{3} \over 4})^2

⇒ a2 + b2 + 2ab = 9169\over16

⇒​​​​​​​ a2 + b2 + 2 × 181\over8 = 9169\over16

⇒​​​​​​​ a2 + b2 = 9169\over16 - 141\over4 = 5165\over16

Now,

⇒​​​​​​​ a4 + b4 = (a2 + b2)2 - 2a2b2

⇒​​​​​​​ a4 + b4 = (5165\over16)2 - 2(181\over8)2

⇒​​​​​​​ a4 + b4 = 2525625\over256 - 2642\over64

⇒​​​​​​​ a4 + b4 = 2525625\over256 - 2642\over64 = 1725617\over256

⇒​​​​​​​ a4+b4+ab3+ba3{{a^4+b^4+ab^3 +ba^3}} = a4 + b4 + ab(a2 + b2)

⇒​​​​​​​ 1725617\over256 + 181\over8 × 5165\over16 = 27256{{27} \over 256}