If x2+x21=A and x−x1=B then least value of BA is

BA=(x−1/x)x2+x21=(x−1/x)(x−x1)2+2 =(x−x1)+(x−x1)2 =p+p2 where p=x−x1 ≥2 using AM≥GM. ∴ Minimum value is 22

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If x^{2} + {1}{x^{2}} = A and x - {1}{x} = B then least valu

Question

If $x^{2} + \frac{1}{x ^{2}} = A$ and $x - \frac{1}{x} = B$ then least value of $\frac{A}{B}$ is

2

2

- 2

22

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Noah Discussed

x^{2} + \frac{1}{x ^{2}} = A

and

x - \frac{1}{x} = B

then least value of

\frac{A}{B}

7 mins ago

Discuss this question LIVE

7 mins ago

\frac{A}{B} = \frac{x ^{2} + \frac{1}{x ^{2}}}{( x - 1/ x )} = \frac{( x - \frac{1}{x} ) ^{2} + 2}{( x - 1/ x )}

= (x - \frac{1}{x}) + \frac{2}{( x - \frac{1}{x} )}

= p + \frac{2}{p}

where

p = x - \frac{1}{x}

\geq 2

using

A M \geq GM .

∴

Minimum value is

22

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Question Text	If $x^{2} + \frac{1}{x ^{2}} = A$ and $x - \frac{1}{x} = B$ then least value of $\frac{A}{B}$ is
Answer Type	Text solution:1
Upvotes	150