Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
If x=5+26, then find the value of xx−1.
2
3+2
32
22
22
Express x as a perfect square: x=(3+2)2. Then, x=3+2 and 1/x=3−2. The expression becomes (3+2)−(3−2)=22.
x = 5 + 2√6
x=(a+b)2=a+b+2ab
Express x as a perfect square: x=(3+2)2. Then, x=3+2 and 1/x=3−2. The expression becomes (3+2)−(3−2)=22.
Students often struggle to rationalize the denominator x1 or fail to identify the square root of a surd.
Represent x as a square
Identify that 5+26 can be written as (3)2+(2)2+2(3)(2). Thus, x=(3+2)2.
x=(3+2)2
Find the value of square root of x
Taking the square root of both sides, we get x=3+2.
x=3+2
Calculate 1/sqrt(x)
Rationalize the expression: 3+21×3−23−2=3−23−2=3−2.
x1=3−2
Evaluate the final expression
Compute xx−x1=x−x1. Substituting the values: (3+2)−(3−2)=22.
(3+2)−(3−2)=22
D is correct because evaluating xx−1 yields x−x1, which results in 22 after simplification.
This type of simplification frequently appears in algebra and trigonometry problems where binomial surds need to be inverted or squared.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download • 100K+ Aspirants