UPSC Prelims 2001 · General Studies

Question 139: Basic Numeracy

Solve the given equations: x² + y² = 34 x⁴ − y⁴ = 544 The values of x and y are

a±4, ±3

b±5, ±3

c±3, ±5

d±3, ±4

AnswerThe answer is (b).

Since x^4 - y^4 = (x^2 - y^2)(x^2 + y^2), dividing 544 by 34 gives x^2 - y^2 = 16. Adding this to x^2 + y^2 = 34 gives 2x^2 = 50, so x^2 = 25 and x = ±5. Then y^2 = 34 - 25 = 9 and y = ±3. Check: 625 - 81 = 544.

Why each option is right or wrong

(a) x = ±4, y = ±3 gives x^2 + y^2 = 25, not 34.
(b) Right: x = ±5, y = ±3.
(c) x = ±3, y = ±5 makes x^4 - y^4 negative.
(d) x = ±3, y = ±4 gives x^2 + y^2 = 25, not 34.

Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2001, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.