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Q139
(IAS/2001)
Science & Technology › Basic Science (Physics, Chemistry, Biology) › Quantitative aptitude topics
Answer Verified
Solve the given equations : x^2 + y^2 = 34 x^4 - y^4 = 544 The values of x and y are
Result
Your answer:
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·
Correct:
B
Explanation
Compute x^4 - y^4 as (x^2 - y^2)(x^2 + y^2). Given x^2 + y^2 = 34 and x^4 - y^4 = 544, we get (x^2 - y^2)·34 = 544, so x^2 - y^2 = 16. Solve the linear system in x^2 and y^2: adding gives 2x^2 = 50, hence x^2 = 25 and x = ±5. Subtracting (or using x^2 + y^2 = 34) gives y^2 = 9 and y = ±3. Thus all sign combinations for x = ±5 and y = ±3 satisfy the equations; the pair (x,y) with x first is ±5, ±3. Therefore option 2 is correct.
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