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SSC CGL 2025 Second Shift 📅 12 Sep, 2025

If x = √((2+√3)/(2-√3)) then determine the value of x² + x - 9?

A
3√3
B
5√3
C
7√3
D
9√3
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SSC CGL
2025 • 12 Sep, 2025 • Second Shift
If x = √((2+√3)/(2-√3)) then determine the value of x² + x - 9?
Correct Answer
5√3
1. Simplify x: x = √[ (2+√3) / (2-√3) ] * [ (2+√3) / (2+√3) ] x = √[ (2+√3)² / (4-3) ] x = 2 + √3 2. Square x: ......
Ref/Book : 1771252791.pdf
Ref. Subject Maths
Chapter -
Ref. Topic Algebra
Pg. No -
💡 Analysis & Explanation
Introduction ▼
1. Simplify x ▼

x = √[ (2+√3) / (2-√3) ] * [ (2+√3) / (2+√3) ]
x = √[ (2+√3)² / (4-3) ]
x = 2 + √3

2. Square x ▼

x² = (2 + √3)²
x² = 4 + 3 + 4√3
x² = 7 + 4√3

3. Put values in x² + x - 9 ▼

= (7 + 4√3) + (2 + √3) - 9
= 9 + 5√3 - 9
= 5√3

Answer ▼
(B) 5√3


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