RRB JE practice question
Two positive perfect squares x and y satisfy √x − √y = 2 and x − y = 40. Find the value of xy.
From a RRB JE Quantitative Aptitude practice set · Quantitative Aptitude
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Correct answer: (A) 9801
Let a = √x, b = √y, so a − b = 2 and a² − b² = 40. Since a² − b² = (a−b)(a+b), we get 2(a+b) = 40 ⟹ a+b = 20. Solving a − b = 2, a + b = 20: a = 11, b = 9. So x = 121, y = 81, and xy = 121 × 81 = 9801.
हिंदी में प्रश्न
दो धनात्मक पूर्ण वर्ग x और y इस प्रकार हैं कि √x − √y = 2 और x − y = 40 है। xy का मान ज्ञात करें।
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सही उत्तर: (A) 9801
मान लें a = √x, b = √y, अतः a − b = 2 और a² − b² = 40। चूँकि a² − b² = (a−b)(a+b), अतः 2(a+b) = 40 ⟹ a+b = 20। a − b = 2, a + b = 20 हल करने पर: a = 11, b = 9। अतः x = 121, y = 81, और xy = 121 × 81 = 9801।
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