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NTPC Graduate Tier 1 2025 Shift-2 📅 06 Jun, 2025

If a² + b² = 111, a × b = 27, and a > b, find the value of (a - b) / (a + b).

A
√(53/165)
B
√(57/165)
C
53/165
D
57/165
Result Summary
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NTPC Graduate Tier 1
2025 • 06 Jun, 2025 • Shift-2
If a² + b² = 111, a × b = 27, and a > b, find the value of (a - b) / (a + b).
Correct Answer
√(57/165)
Finding the Difference: Utilize the algebraic identity (a - b)² = a² + b² - 2ab. Substituting the known values yields (a - b)² = 111 - 2(27) = 111 - 54 = 57......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Mathematics
Chapter -
Ref. Topic Algebra
Pg. No -
💡 Analysis & Explanation
Finding the Difference ▼
Utilize the algebraic identity (a - b)² = a² + b² - 2ab. Substituting the known values yields (a - b)² = 111 - 2(27) = 111 - 54 = 57. Given that a > b, we take the positive square root: a - b = √57.
Finding the Sum ▼
Use the related identity (a + b)² = a² + b² + 2ab. Plugging in the numbers gives (a + b)² = 111 + 2(27) = 111 + 54 = 165. Taking the square root gives a + b = √165.
Calculating the Ratio ▼
The required fraction is (a - b) / (a + b). Substituting our calculated roots gives √57 / √165, which can be combined under a single radical.
Conclusion ▼
The final simplified value is expressed as √(57/165).
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