If - - 1a - - and - - 1a - - find the relation between - and -

We have 𝒂 + 1a = 𝒎 and 𝒂 − 1a = 𝒏 Squaring and adding both equations, (𝒂 + 1a)^2 (𝒂 − 1a )^2 = m^2 n^2 = gt; 4 × a × 1a = m^2 n^2 = gt; m^2 n^2 = 4 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Distinguishing between Conics from General Equation and Eccentricity

If 𝒂 + 1a = ...

Question

If $a + \frac{1}{a} = m$ and $a - \frac{1}{a} = n,$ find the relation between $m$ and $n .$

Open in App

Solution

We have $a + \frac{1}{a} = m$ and $a - \frac{1}{a} = n$
Squaring and adding both equations,
${(a + \frac{1}{a})}^{2} - {(a - \frac{1}{a})}^{2} = m^{2} - n^{2}$
$=> 4 \times a \times \frac{1}{a} = m^{2} - n^{2} => m^{2} - n^{2} = 4$

Suggest Corrections

Similar questions

Q. If

x^{2} - 4 x - 12 = (x + m) (x + n)

, then find the value of

(m + n)

Q. If

x^{2} - 4 x - 12 = (x + m) (x + n)

, then the value of

(m + n)

is _____.

Q. If 𝒙 and 𝒚 vary inversely, find the values of 𝒍, 𝒎, and 𝒏.

Q. In the given figure, if 𝒍 || 𝒎, 𝒏 || 𝒑 and ∠𝟏 = 𝟖𝟓°, find ∠𝟐.

What term should be subtracted from each term of the ratio𝒂 : 𝒃 to make the ratio 𝒎 : 𝒏?

Join BYJU'S Learning Program

If a+1a=m and a−1a=n, find the relation between m and n.

We have a+1a=m and a−1a=n Squaring and adding both equations, (a+1a)2−(a−1a)2=m2−n2 =>4×a×1a=m2−n2=>m2−n2=4

If $a + \frac{1}{a} = m$ and $a - \frac{1}{a} = n,$ find the relation between $m$ and $n .$

We have $a + \frac{1}{a} = m$ and $a - \frac{1}{a} = n$
Squaring and adding both equations,
${(a + \frac{1}{a})}^{2} - {(a - \frac{1}{a})}^{2} = m^{2} - n^{2}$
$=> 4 \times a \times \frac{1}{a} = m^{2} - n^{2} => m^{2} - n^{2} = 4$