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If a+a1=8, then a2+a21=?
64
68
66
62
62
For x+1/x=n, the value of x2+1/x2 is simply n2−2. Here, 82−2=64−2=62.
a + 1/a = 8
(a+a1)2=a2+a21+2
For x+1/x=n, the value of x2+1/x2 is simply n2−2. Here, 82−2=64−2=62.
Students often square the expression and forget to subtract the middle term 2(a)(1/a)=2, resulting in the incorrect answer 64.
Square the given equation
To find a2+1/a2, start by squaring the given expression a+1/a=8.
(a+a1)2=82
Expand using (x+y)2
Expand the left side using the identity (x+y)2=x2+y2+2xy. Here x=a and y=1/a.
a2+a21+2(a)(a1)=64
Simplify and solve
Since a×(1/a)=1, the equation simplifies to a2+1/a2+2=64. Subtracting 2 from both sides gives the answer.
a2+a21=64−2=62
D is correct because applying the identity (a+1/a)2=a2+1/a2+2 with a+1/a=8 yields 64−2=62.
This is a fundamental concept in SSC and Railways exams. Remember the pattern (x+1/x)2=x2+1/x2+2 for quick solving in competitive tests.
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